Louden Wilde
Muse
I suspect the actual argument has been unstated (and perhaps unrecognized) so far, but goes something like this:
Females should have the rights/spaces/representation (etc.) that have evolved over time, and that feminists have fought for and are still fighting for... And transwomen should be able to piggy-back on these norms and efforts by self-ID alone.
I think you're correct (that this is the unstated argument) - which is really that there should not be any sex-specific rights/spaces/etc., but that any segregation should be based on gender. I've seen many trans-activists say this on twitter. Of course, it's never framed as saying that there should be no female-specific rights, rather that TW/TIMs are entitled to those rights (which of course negates them by definition).
There seems to be an increasing movement (going along with self-ID) that says presentation isn't necessarily important. So the answer to that last question is 'because you identify as a woman'. If we accept the Eddie Izzard/gender-fluid model, the answer may be because you ID as a woman that particular day.After all, without a distinct norm in law and custom, transwomen have nothing to transition to. At that point, transwomanhood becomes just another expression of masculinity, alongside jocks, frat boys, hipsters, metrosexuals, and effeminate men. If you're not allowed in a women's shelter because you're wearing a popped collar and a backwards ball cap, why should you be allowed in a women's shelter because you're wearing a dress and makeup?