"socialization is inherently transmisogynistic" to me seems like one of those beliefs that came about when a valid criticism of how the concept of "socialization" was used, went through the discourse grapevine. yeah, socialization is literally just the process of internalizing social constructs. its a sociological term that isn't even exclusively about gender; its about how reality is socially constructed in general, including gender
actually i'm gonna be petty and quote my man Peter Berger (from The Social Construction of Reality: A Treatise in the Sociology of Knowledge, which is unfortunately very androcentric in its language, it's from 1966):
The individual, however, is not born a member of society. He is born with a predisposition towards sociality, and he becomes a member of society. In the life of every individual, therefore, there is a temporal sequence, in the course of which he is inducted into participation in the societal dialectic. The beginning point of this process is internalization: the immediate apprehension or interpretation of an objective event as expressing meaning, that is, as a manifestation of another's subjective processes which thereby becomes subjectively meaningful to myself. This does not mean that I understand the other adequately. I may indeed misunderstand him: he is laughing in a fit of hysteria, but I understand his laughter as expressing mirth. But his subjectivity is nevertheless objectively available to me and becomes meaningful to me, whether or not there is congruence between his and my subjective process. Full congruence between the two subjective meanings, and reciprocal knowledge of the congruence, presupposes signification, as previously discussed. However, internalization in the general sense used here underlies both signification and its own more complex forms. More precisely, internalization in this general sense is the basis, first, for an understanding of one's fellow men and, second, for the apprehension of the world as a meaningful and social reality. [...]
Only when he has achieved this degree of internalization is an individual a member of society. The ontogenetic process by which this is brought about is socialization, which may thus be defined as the comprehensive and consistent induction of an individual into the objective world of a society or a sector of it. Primary socialization is the first socialization an individual undergoes in childhood, through which he becomes a member of society. Secondary socialization is any subsequent process that inducts an already socialized individual into new sectors of the objective world of his society. [...]
It is at once evident that primary socialization is usually the most important one for an individual, and that the basic structure of all secondary socialization has to resemble that of primary socialization. Every individual is born into an objective social structure within which he encounters the significant others who are in charge of his socialization. These significant others are imposed upon him. Their definitions of his situation are posited for him as objective reality. He is thus born into not only an objective social structure but also an objective social world. The significant others who mediate this world to him modify it in the course of mediating it. They select aspects of it in accordance with their own location in the social structure, and also by virtue of their individual, bio graphically rooted idiosyncrasies. The social world is 'filtered' to the individual through this double selectivity. Thus the lower-class child not only absorbs a lower-class perspective on the social world, he absorbs it in the idiosyncratic coloration given it by his parents (or whatever other individuals are in charge of his primary socialization). The same lower-class perspective may induce a mood of contentment, resignation, bitter resentment, or seething rebelliousness. Consequently, the lower-class child will not only come to inhabit a world greatly different from that of an upper-class child, but may do so in a manner quite different from the lower-class child next door.
the problem comes when "male socialization" (or "afab socialization") is weaponized against trans people, as a way of doing gender essentialism without being explicitly bioessentialist, or when its used in a very shallow way. gender socialization is not "society shoots the Girl/Boy Beam at you and you Think Like A Girl/Boy forever." it is a complex and only semi-purposeful social process. on a sociological level we can describe trends in people's experiences (for example, people seen as girls being pushed towards caretaker roles, people seen as boys being punished for crying) but there are a lot of trends, including amongst queer (gay, gnc, trans, intersex) people.
on top of that, individual experiences with socialization are rarely going to fall neatly into any categorization, because there are a lot of factors at play in every person's life that shape how they are being socialized. and then there's also the fact that not everyone reacts the same way. one person seen as a girl may easily internalize the expectations of the Girl Role and perform that role very happily, while another person seen as a girl may struggle greatly or be actively resistant. that doesn't mean they aren't still experiencing socialization, it just means its more complicated than, again, getting shot with the "Think Like A Girl" beam.
so yeah. "socialization is inherently transmisogynistic" in my opinion, is just the result knowing through the grapevine that "gender socialization" is something often used by TERFs to be transphobic, and making assumptions without really understanding sociological theory.