The claims by "trans" activists are so blatantly postmodern, so riddled with incoherence, that most of the time I don't bother even to try to point out the incoherences. There was a good article in, I believe, National Review that did so a couple of months ago, but unfortunately I didn't save the link. If one of my readers happens to find it, let me know. I think it may have been by Maggie Gallagher.
Here's one bit of the incoherence that came up in a thread at W4 where a commentator was asking about the best arguments (??) of the trans activists. Short version: There aren't any. Anyway, this commentator suggested that, while it seems far-fetched to say that gender identity can be constructed based solely on a person's subjective feelings, maybe it isn't so far-fetched to say that someone "is" a particular "gender" based on "social role," which might differ from biology. At least, so I understood him to suggest as one of the "best" representations of the trans position.
But as I point out in the comment here, that does not make any sense, because society never spontaneously assigns a person a "social role" that is utterly in conflict with his unambiguous biological sex. Setting aside extremely rare cases of true biological disorders in which a mistake is made at birth because the child biologically (externally) appears to be the opposite biological sex from his genetic sex, no one just "gets" a "social role" of being a man when he is biologically a woman. No biological woman just "gets" a "social role" of being a man. It doesn't happen. Something has to kick off the process in society. The person has to complain of "gender dysphoria," and get "treatment" that includes making other people use new pronouns, or parents or psychologists have to get signals that they take to mean that, in the mysterious trans meaning, the person "really is" the opposite gender from his biological sex, and then that small coterie of people starts trying to impose this new understanding on everybody else. But they aren't society. Prior to being told that Bobby is now a girl, society was just going on its merry way treating Bobby as a boy. Bobby doesn't have a "social role" of being a girl until society is forced to start calling him "she" under threat of punishment and so forth or until society is fooled by extreme (and immoral) medical procedures and drugs foisted upon Bobby so that society (or those members of it who didn't know Bobby before) falsely believe that Bobby (who now goes by "Sarah") is biologically female. If Bobby/Sarah succeeds in passing himself off as a woman, at that point "society" may assign him a female role, but that's only because of a successful deception concerning biology, not because he originally "was" a woman in the sense of having "woman" as a societal role. He didn't. That's why he had to "transition."
So there is no hope for the trans agenda in logic from a mantra like, "Gender identity is socially constructed," because that provides no rationale for society's giving a person a social role that he didn't originally have in the first place and because society, left to itself, will spontaneously assign a biologically unambiguous person a social role (whatever it may be in that society) that agrees with his biology to begin with. One could just as well tell the trans activist who mouths this "argument," "Fine, then, I guess Bobby isn't really a girl, because look at all the people who have been calling him 'he' all this time. He has the socially constructed role of a boy, so that means he's a boy. Case closed."
The trans activist has to insist upon a process of redefining a person as "really" being something other than what he biologically is without the support, initially, of either biology or social role.
None of this, of course, will stop activists (and their dupes) from talking sagely as if a phrase like, "Gender identity is socially constructed" supports their agenda. But logically, it doesn't.
Tony, my blog colleague at W4, comments here pointing some of this out as well.