Do transwomen exist? Of course they do. And it follows from their very existence that they are - one and all - men.
Why so?
... Because, to begin with, humans can't change sex. So, if a transwoman is a man who has changed sex (and given that men are human(!)), there can be no such thing as a transwoman. (But there is ...)
Contraposing, and equivalently, if transwomen exist, and a transwoman is a man who has changed sex, then it is possible for a human to change sex. But humans can't change sex. So there are no transwomen. (But there are ...)
Of course, if a transwoman isn't a man who has changed sex but just a man who would like to change sex, this argument won't work.
So what follows? - Just that if you believe transwomen exist, you have to believe transwomen are men. To claim transwomen are women is to claim transwomen don't exist. Just logic.