No. It's not. That's not how language works. Clothes horses are not horses. Family trees are not trees. Loan sharks are not sharks.
Just because its possible to prefix "woman" with another word doesn't mean you've identified a new type of woman.
And what I find so deeply frustrating about this linguistic sleight of hand is that it leaves us arguing stupid semantics instead of real issues. I really do support trans people. I really do want trans people to live free of discrimination and bigotry. But acknowledging that there are (only a very few) occasions where the inclusion of trans women conflicts with the rights and safety of women, and asking to have an honest, constructive conversation about that, is not hateful.
Nor is this about cultural stereotypes. In fact, the most obvious criticism of much of gender identity ideology is that it leans so heavily into gender stereotypes. We should be running as fast as we can from the idea that a male child who likes "girl things" or likes to wear dresses is literally a girl. Yet here we are in 2022 calling arguments like these "progressive".
Lastly, I'm so sick of this deeply racist analogy. I wish I could say "let's settle this once and for all," but I've no doubt some other bright spark will come up with it at some point. "Woman" is just a word that means adult human female. Black women aren't a type of woman. Black women are women whose skin happens to be black (or actually brown).
What you're trying to argue here is that trans women are women who just happen to be male. It's a category error. It's like trying to argue that motorcycles are cars that just happen to have two wheels and no roof and no windows and no seatbelts and not steering wheel and completely different seats. No, they're motorcycles. And that's okay. They're subject to different regulations and use the road in different ways sometimes and they're both perfectly valid in their own ways.
The question of whether a black woman is a woman only makes sense under the assumption that the default, "real" kind woman is a white woman. Of course, when people were making these arguments, that's exactly what they thought. I'd just hoped that in 2022 there weren't still people ignorant enough to think this way. I guess I was wrong.