Please read a little more carefully. You've based an entire argument here off something I didn't say.
I actually said that gender is complicated. To be precise, so complicated the the term is almost meaningless. Far from being 2 genders, there are ~8 billion. No two people express their gender and their identity in the same way. There's no single word that expresses my combination of masculinity and femininity or that expresss yours. In the end, we're basically talking about a personality as viewed through certain stereotypes.
What I said was simple, was that a woman is an adult human female. Just as a lioness is a female lion or a vixen is a female fox. I still don't understand why this has become controversial.
Trans people exist, they deserve the same rights and dignity and safety as everybody else. As I've mentioned elsewhere, when I meet trans woman in real life, I don't continually refer to them as trans. But the idea that it's hateful to remain aware of the indisputable fact that they are trans when it's relevant is so bizarre to me. And nobody has ever explained it.