It shouldn't be that hard of a struggle. Just start with "What constitutes a transsexual, and how do you tell that they're transsexual?"
Does Alex Drummond count as a transsexual? What about Eddie Izzard? What about Darren Meragee? Jessica (Jonathan) Yaniv?
Where do you draw the line? Does a male only count as transsexual if they've had a complete penectomy and orchiectomy, and if so... who does the checking? What if they've had facial feminization surgery but have a fully intact and functional penis and testicles - do they count as transsexual? What if they have a full beard and haven't taken any estrogen at all?
At some point you end up with a situation where literally any male who puts on some chapstick and says the magic phrase "I'm trans" has to be counted as being transsexual.
And at that point, you've opened up the female facilities to any man who wants to be there, and you've simultaneously removed the ability of females to object to this gross violation of our boundaries and consent.