Gendered socialization is when people call you a girl right up until you say you're a girl, and then you become a man
One thing that inevitably comes up in discussions about trans people is our experiences before transition and how those shape us. Supportive cis people are often curious about the unique perspective that having been on both sides of the metaphorical tracks gives us, though how well they express that is variable. Unfortunately because this is the internet and involves trans people, what is more common is using the concept of gendered socialization as a cudgel. 
Bear with me I'm going to go about this in a bit of a circuitous way.
They say write what you know
One of the reasons I do want to write about this is because none of my childhood experiences fit cleanly into the standard scripts for gendered socialization, neither the AGAB supremacy scripts or the ones commonly described by other trans people (though there are definitely a few that echo). Some of that is down to being non-binary, some to oddities of how I was brought up. Nonetheless.
Narratives
A selection of gendered socialization narratives follows. They depict a number of perspectives, both those commonly believed by progressives and those believed by social conservatives. One key point is that none of these are necessarily wrong, for some subset of people, though some are...suspect. It's also a fairly white-centric set of perspectives, both to avoid straying too far out of my lane and because these are intended to reflect proposed dominant gendered socialization narratives from the cultures I grew up in.
Fair warning. I am going to use "boys" and "girls" as a proxy for assigned sex here at times, for rhetorical effect. Skip to the next section with a non-numbered, lavender header if your brain is going to hate that.
1. Boys will be boys
This is the classic "male privilege" script. Boys get cut slack on behaviour, they get a free pass from authority figures and have it reinforced that they have a right to rule, even if they get treated badly now. I expect most people to be familiar with this one, and so I'm not going to belabour it. 
2. Girls are better
Girls just have a better intuition for social things than boys. They're less messy, they follow the rules better, and they don't get weird after puberty. Sure, they're never quite as exceptional as some of the boys, but they're far more consistently hard workers. Boys are just lazy. Though some girls just don't understand that they have to be focused on what really matters. Those girls who are so vain about their appearance, or get so preoccupied with social things, or don't care at all, they always run into problems, and honestly they should know better by the time they grow up. Who's script this is is a bit more subtle.
3. Boys are defective girls
This is the common "social justice skeptic" response to the above two. Boys in current society, particularly during their education, are treated like defective girls. Boys are treated as inherently predatory, or at risk of being predatory, and are suspect by default, while girls are seen as pure and well-behaved and get treated better, particularly because doing so is seen as countering boys' "privilege". Boys are penalized for not being able to sit still like girls at as early an age. They are seen as troublemakers in a way that that girls aren't. This is also not actually wrong, especially when it comes to boys from marginalized backgrounds, or neurodivergent boys.
4. Girls must be good (or else)
This is the flip side of the above two in its way. Girls are expected to meet higher standards of social behaviour. They are expected to be helpful, even when that puts them in the line of fire. They are expected to respond with grace to bad behaviour from others. And if they do all of that well, they will be rewarded with more of the same, but also be trusted and respected, unless they talk back too much. One thing I will note here is that you can see how this is entirely compatible with the perception from the above. The boy who sees the above simply doesn't see the cost or the implied Sword of Damocles, only the reward.
5. Boys only get to be boys if they follow the rules
While some boys get to just be boys, that only happens if you're sufficiently gender and culture conforming. If you aren't you get treated as disposable support scaffolding for those who are. There's two tracks to this one, depending on whether you commit the cardinal sin of being effeminate or not. The "effeminate" track is the one described by many trans women and gay men, in particular trans women who liked men. You get used by men on the down low, even as a child, and the expectations and privileges of boyhood or manhood are held above you and used as a cudgel to reinforce your status as faggot, fairy, tranny. If you aren't obviously effeminate, you're still not off the hook, though. You're seen as both weak and useless and a potential predator to girls as you hit puberty. If you're sufficiently smart in a way that's legible, then maybe adults might value it, but your peers probably don't, except to the extent that they can hold acceptance over your head as a way to get you to do stuff for them.
6. Girls who don't grow out of acting like boys must be put in their place
Being a tomboy is pretty accepted for younger girls and has been for a long time. But you're expected to grow out of it. If you don't, then, well, you've got to be reminded of what you really are. Effeminate "boys" get "if you act like a girl, then I'm going to treat you like a girl." Masculine "girls" get the flip side, "You think you're a boy, that you're going to be a man? Well I'll show you." This is the track that a lot of trans men, transmasc non-binary people, and butch lesbians describe. Girls are permitted a little masculinity as a treat, it's even good for her to be "one of the boys," to a point. But once she hits puberty, she's got to look fuckable presentable, and she can't be doing anything that might cut her off from being a mom later.
So...
These are really all just views of an evolving cultural landscape from different perspectives and subcultures within that. If you've heard me talking about my own childhood at all, you know that I grew up in a weird set of cultural intersections. My parents are devoutly religious, environmentalist, pro-immigration, economically liberal/leftist, socially conservative, gender egalitarian Canadian Baptists who have life sciences backgrounds (as well as some academic theological training), believe in evolution, went to Africa to do missionary work, and then both got doctorates at an Ivy League university. You can almost certainly doxx me from that description alone. Nonetheless I think it needs to be clear that I did not have what you'd call "average" parents. My parents are brilliant, driven, and deeply compassionate people. While I don't have a great relationship with them now, in part because of how they reacted to me coming out as trans, that is a small mark on the overall picture. And that picture is a bit of a weird one as far as it comes to raising a "boy" who was basically every way in which my parents were different from the average combined into one person. Both of my parents also have what I'd call "sub-clinical" ADHD and autistic traits. Neither got diagnosed, or thinks of themselves that way, but nonetheless those tendencies are quite clearly there, and in ways that are pronounced relative to most people, and while I'm not going to address it head on, it's probably quite relevant for my socialization.
Assigned Normal at Birth
One thing that I notice looking backward is how little slack my parents gave me compared to seemingly everyone else on the planet. I grew up thinking of myself as rude and thoughtless and utterly lacking in social grace, while my teachers universally described my behaviour in glowing terms, even those I got into arguments with, and the same for pretty much all other adults. My parents had expectations of me that more accorded with the expectations for girls discussed in the previous section than any of those for boys. Whether that was out of an egalitarian mindset, or what, I still have no idea. The rest of society...well that varied.
I remember, when I started piano lessons, my parents giving me what was in retrospect a "how to know and report if you are being abused sexually by a man" lecture. I thought it odd at the time, didn't really understand it, and perhaps many parents gave that lecture to their young boys, but it stood out. My parents were not helicopter parents in the slightest, I was given comparable or more freedom than others my age, with a couple of specific exceptions, and this was all in an era before ubiquitous cellphones for children and teenagers, but they were always, even well into high school, at least a little worried about me in ways that I can only really map onto them seeing me as a potential victim of (sexual) abuse. And of course it's not that boys (much less trans girls) don't get sexually abused, but my parents were protective of me in a specific way that is atypical among the men I know.
We're going to start at around age 8 or so, as my memory is less good before that. But in the broad strokes, I'll paint a picture of a little child with bright blue eyes and a buzz cut who loves reading, loves animals, science, Lego, music, and math, who will be extremely shy unless they think you're interested in hearing about something new they've learned and will then proceed to talk your leg off, and who gets along with girls at least as well as boys. I was a very small child. From my own recollection of childhood visits to the doctor, I was basically one tick off being so short and light for my age that it was a medical concern. When we moved from Africa to the US and my parents went to enrol me in the 3rd grade at the local elementary school, as made sense for my age and what I'd completed in homeschooling, the official tried to nudge my parents toward enrolling me in 2nd grade instead, apparently because I was so small and quiet. Thankfully my parents didn't go along with this, but it sets the stage for a few things.
My experience in school at that age and those following was one of confusion and struggling to find a place. Most boys saw me as kind of a nuisance or an accessory to whatever they were doing. Girls would include me in activities more often. I made friends with some neighbours (two girls, and then a boy) and eventually in a year or two found some boys who I did get along with, nerdier quiet types. But there I was also usually kind of an accessory, I was playing the kinds of games they wanted, though at least those were mostly games I liked.
Math and (lack of) "Protagonist License"
An odd sideshow there which ends up being illustrative was my brief placement in remedial math. The placement test they gave deliberately included material you weren't yet expected to know, expecting you to skip problems that were too hard and complete as many as you could. I had never taken a test like this and was too shy to ask for guidance, so I got stuck trying to work through an early problem I didn't know how to do and ended up with a low score. I was frustrated, as after the test someone had explained the correct approach, and felt rather shortchanged. I talked to my parents when I got home, and they basically said to accept my placement but do well and then they might bump me up next year. This would be a recurring theme with my parents. Because for all that my parents are brilliant, driven people, they are humble to a fault, especially my mother. You must never ask for anything like special treatment or do things that might imply that you think you're better than other people. You must simply work hard and prove yourself worthy. I think I lasted a month in remedial math, quietly getting everything right in a fraction of the time of any of the other students, before someone finally decided this was ridiculous and moved me back to standard math. The following year I went into the advanced placement track.
Unfortunately this also applied to other areas where I wasn't "normal" either. I couldn't get too far ahead in school for "socialization" reasons, plus it would be arrogant to think I was a genius or something. Neither could my struggles to socialize with my peers mean anything other than that I was a bit shy and anxious, nor could the fact that I was incredibly disorganized and forgetful about temporal needs be anything other than a quirk worthy of a remark about being a "little absent-minded professor." After all, my brother was autistic and disabled. I was normal, if smart. I just had some growing up to do. As to the title, that's something I need to explain elsewhere. ‌ I feel I should also note here that while my parents probably come off somewhat poorly in this to say the least, that's really not representative. They very demonstrably loved and cherished my brother and I greatly. They were warm, compassionate, and accommodating, and were deeply but not overly involved in my life. They just weren't perfect, and we're running right smack into all the imperfections here.
I did ultimately find a place, of sorts. And was fairly happy in it. I was bright, got along well with my teachers, and had friends. I taught myself to program, learned to solder, make circuit boards, do woodworking. I got into Dungeons and Dragons, read hundreds and hundreds of books, and played Age of Empires. I learned to play the trombone. I played video games with my piano teacher's kids while I waited for my parents to pick me up after my lesson. The kid I was closest in age to there later transitioned in the other direction to me, long after we moved away.
As I grew older I noticed I gradually and then abruptly lost social connections with girls, particularly once kids started puberty. It confused me deeply at the time, because while I understood myself as a "boy" by virtue of my anatomy and genetics, I struggled to see gender or sex as a fundamental point of division, though I did come to understand fairly quickly that other people did, and that having interests too out of step with your sex was generally not a good idea. Fortunately for me I liked enough "boy" things that this wasn't too much of a sacrifice. But I did have to be careful to not be too interested in French class, or poetry, or sewing, or cooking when I was at school. Nonetheless, I still got called a "pussy" and a "faggot" by some other children well before my sheltered religious ass knew what either of those meant except literally or why they were supposed to be insults.
In some ways I was thankful when I finally developed an interest in romance and started dating a girl in Grade 10, because that was a ticket back into normal interactions with them (both with my girlfriend and platonically with her friends and others now that I was both vouched for and off the market). ‌ The circumstances of that are quite funny in retrospect. There were two girls in my class I had a crush on, though I only half-realized it. I ended up doing a group project with both of them, and then one of them all but asked me out, and I managed to take the hint for once in my life.
While puberty took a little longer to become evident for me than for many of my peers, it did very much occur. My voice dropped smoothly from the extremely high soprano I described in middle school as "my squeaky mouse voice" to a tenor or a baritone. And I got stronger. That one took some getting used to. Because one thing I have glossed over is how I sometimes got into fights as a kid. It didn't happen a lot, and usually it was because someone was picking on me or another kid, but it did happen. I pretty much never got in trouble, in large part because nobody could see me as a threat, nor was I one. That changed with testosterone puberty. All of a sudden, I could actually hurt someone, and I did once or twice, before I got a better handle on my temper. And while I was always, even after that point, seen as oddly safe relative to other teenage boys (or men), I did finally get why some of the dynamics had changed in ways that had confused me previously, particularly as I realized that my girlfriend very much did not have that same strength, despite being roughly my height and relatively more athletic. I didn't like which side of that dynamic I was placed on, but I didn't know what else to do at the time. And then I graduated high school and everything sort of fell apart for most of a decade. And that's another story.
Narratives Redux
You can sort all this into one of the "male" narratives from earlier if you squint. Because the expectations came from my parents more than society and because I wasn't obviously feminine in a way that garnered negative attention, there's large aspects of this which look like "nerdy autistic white dude" childhood and do not look like the transfeminine childhood narratives I have heard from others (in many ways I am quite thankful for this, because it means my childhood was free of sexual abuse). My parents would and have asserted that I was a very typical boy, and I haven't said much in this about dysphoria directly.
If you want to know where I started imagining fictional universes where I or a self-insert was either a woman or some form of intersex, that would be at about three or four paragraphs up, around the start of puberty. A bit later would be the last time I was really comfortable in my body for a long time.
Certainly I benefited from being seen as a boy. While this was the beginning of the era of "Women and girls in STEM" programs, there was definitely a way in which I was allowed to be into engineering, computers, and technology that was discouraged for girls. I also think I was cut some amount of social slack because I was seen as a boy, which meant I didn't have to mask my own neurodivergence as hard, though equally my parents taught me more than enough to be quite good at it. And being as into video games as I was wasn't something that was permissible for girls. This was actually more enforced by other girls and adult women than anything, as far as I saw. While video games were seen as a bit childish and unserious for anyone to be really interested in beyond a certain age, girls were supposed to be more mature than boys, and that meant not being into video games. Boys that I knew mostly loved girls that liked video games, they were happy to have a shared interest. I only really saw nasty gamer/nerd sexism online, and mostly later. And while my parents scoffed at the idea of me being "special" by virtue of my intelligence or technical skills in a sense that made me better than other people, others definitely didn't, they were very impressed and said all sorts of things.
But if you think it's that simple, read through it again. Listen for the ways in which I cut off myself from things I loved in order to avoid mistreatment for reasons I barely understood. One of the reasons I almost welcomed puberty and the voice drop that I'd later regret—the voice drop I, barring some major advancements in the field of vocal feminization surgery or giving up my singing voice, have to compensate for on some level for the rest of my life if I want to get read consistently as anything other than a man—was because my pre-pubescent voice was so high that I felt like it prevented people from taking me seriously. Because if anything defined my life before puberty, it was a never-ending struggle to get people to take me seriously as a person, and treat my ideas and thoughts like they would an adult's on some subject where understanding of the facts mattered.
Elizabeth Holmes, I get it, at least that bit. Not the fraud, though.
And you can see how I never really felt in community with boys or men. It was the class I was compulsorily sorted into, but not one I had any attachment to, nor did I (nor really could I) take advantage of the benefits except by accident when some of my natural inclinations sort of aligned. Where I chafed, it was in many of the same ways that my mom (brilliant, stubborn, and opinionated) in retrospect clearly chafed against her own cultural programming, which she also pushed onto me. There's an angle here where my mom saw something in me she recognized intuitively but didn't have a good name for, and it made her scared for my sake, and so she tried to equip me as best she knew how for how to handle it. And in some ways I like that narrative in part because it makes her struggle to accept me of a piece with internal struggles around her own relationship with her sex/gender and how society treats women, rather than just bigotry leading her to torpedo her relationship with her eldest child rather than repair it, when they wanted and needed her love and acceptance the most.
Born this way
I think the fact that I had a relatively good childhood free of obvious trauma makes it if anything clearer how much the "male socialization" both only sort of occurred (even if you take my unusual parents out of the equation) in the standard way because I was—in spite of being someone with lots of "masculine" interests and skills, not in fact like a typical boy—and largely failed to "take", mostly just causing frustration and some distress. And all this was still true even though I was completely unaware of trans people until well into my teens, while also being in a household that was both highly egalitarian and religious. If I had been much more feminine, I think they would have been broadly okay with that, though even more worried for my well-being at the hands of other children and adults, and might have been convinced to do something harmful to "protect" me. In short, if protecting a child from almost all of the societal forces that people have claimed cause transness would have worked, I would not be trans, because I was so protected, through a very unusual confluence of factors, particularly in my early years.
I do think I was born this way. I did not have a choice, not really.
I was always non-binary, it just took a while to actually figure that out.
But I shouldn't have to prove that, nor defend it.
As to why I feel I must make that defence, that comes down to the dynamic that drives this discourse.
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Contamination
I owe a fair bit of my thinking on this to Julia Serano, with her "stigma contamination" model of certain kinds of bigotry.
We like to think that either we are fighting this mentality or, if we are a bit delusional, that we have beaten it. But in many progressive, liberal, or leftist spaces, we really just spin it around a little. People shit upon their political enemies for seeming gay, portray them as effeminate, and it's fine because we know it bothers them, and they're such evil hypocrites. As much as I have utter contempt for someone like Nick Fuentes, the way people often talk about the little fascist does not make me feel safe, because it echoes many of his ways of seeing the world, sexuality, masculinity.
We also sometimes turn that marking and contamination fear around and apply it to men, and anyone suspected of being contaminated by men, or having too much sympathy for men, which inevitably ends up including trans people. The most obvious and extreme form of this is TERFism, obviously, but less blatant and extreme versions of the same mindset persist. I also will not say this isn't at least on some level motivated by a hatred of men for some people. Not all, as we've seen with TERFs and "gender critical" types, many are happy to make common cause with misogynistic men against trans people and much of their hatred comes just as much from the more conventional version of this dynamic, but some. Of course for trans men the dynamics get if anything weirder. People will trust them for reasons that risk misgendering them, will deny them agency in discussions about this very dynamic while claiming to be speaking in their defence, while also distrusting them for their "opting into" manhood, and so on. I'll let them talk at length on that, if they want to. But more than just one specific re-targeting of this mentality is the overarching fear of the oppressor coming in to the better place, and a resulting need to stamp that out in whatever form we find it, and prove to each other that we are not that, even as we tear each other apart over a million tiny sins.
And so it saddens me the most when trans people deploy this shit against each other, the general pattern as well as the specific socialization accusation form of it. I'm not going to bring up examples. Some I have found...amusingly if frustratingly ironic, others absurd and beyond the pale, from any direction. Part of why it saddens me is because I feel like we all should know better, but we're all human, so we don't. And another part is because we are all so vulnerable. We do so much damage to our communities, our often threadbare support networks with this and other fights. Even the ones with good cause do harm we can't necessarily afford right now.
Socialization is in some ways a flashpoint because this shit is complex, it's so specific to each person and how they grew up. There are many trends, but few if any universals. And it gets right into the bits of us we're told to be ashamed of the most. The stuff we've maybe hid from our doctors to access care we needed. The stuff we don't put in the autobiography because we know how it looks, or if we do gets thrown back at us later. The accusations bigots make against us which we feel we risk substantiating if we don't frame things a certain way. The need to prove that we are good and not evil. Oppressed and not oppressor. Free of contamination. And in part because our experiences all differ and because this is so charged by society and our own self-doubts, fears, and shame, we lose sight of each other and end up striking at shadows and hitting our friends.