What about a man who loses his penis in an accident? Is he no longer a man? Would he still be allowed to identify as a man? Would a woman born without a vagina still be allowed to identify as a woman?
As a rough approximation, yes.
> What about a man who loses his penis in an accident?
He's a man who lost his penis. Statistically insignificant and doesn't change the fact that the vast majority of humans, by far, have either a penis or a vagina.
Again, the exceptions do not invalidate the norm that we all know is true. For thousands of years we've understood human reproduction and the role of males with penises, and females with vaginas.