1/ I've yet to find a glossary of LGBTQ+ terms and gender identities that will define the terms "woman" and "man." They use the terms freely as part of the definitions of OTHER "identities", but they never actually define them on their own. Go ahead, search for yourself.

2/ The closest I could find has to be inferred from other definitions. For instance, some lists define a "transgender woman" as someone who was assigned male at birth but who "identifies and lives as a woman."

3/ From this definition you can infer that a woman is therefore "someone who identifies and lives as a woman." But this contains 0 informational content, since identities are entirely subjective and therefore suffer the problem of being "private language." https://en.wikipedia.org/wiki/Private_language_argument

4/ And "living as a woman" suggests that there are bounded criteria for how a woman can live. And if that's true then that means there are certain ways of living that are incompatible with womanhood. But then it's insisted that there is no right or wrong way to live as a woman.

5/ The terms "woman" and "man" then contain no information. They're entirely meaningless utterances. Just noises some people claim to identify with.