What is a woman? I don’t think there’s a clear answer to that question. But I believe it’s an identity you feel (rather than dictated by sex organs) and I would recognise anyone as a woman if that’s how they chose to identify.
I'm sorry @StolenCookie, but that isn't a good enough answer.
"Women" is a word for a group of people making up about half the human population. In order for that word to have any meaning or use, the people in that group need to have something in common.
What do women and trans women have in common, which makes them the same as each other and different to men, and justifies them using the same toilets and changing rooms, being housed in the same prisons and competing in the same sporting categories?
If you think it is that they share the same identity, you need to be able to explain what the features of that identity are.
Because I for one do not have a clue what trans women are identifying with.
If you ask me how I know I am a woman, I will tell you that it is because I am biologically female. I have a vagina, ovaries, a uterus and breasts. I have two X chromosomes. I menstruate. I have grown a human inside my body. I have not ever had a penis or produced sperm.
I do not know what trans women are identifying with, but it clearly isn't that.
And I am not identifying with anything other than that.
I certainly do not identify with liking the colour pink, playing with Barbies, shopping for pleasure, not being able to open jam jars, wearing dresses and makeup, not being able to parallel park, or any other sexist stereotypes associated with being a woman.
Once you remove female biology from the equation, all you've got left is sexist stereotypes.