That's not why people say that "trans women are women". They say it because of the existence of gender dysphoria--that is, the person is psychologically female and finds it profoundly distressing to be trapped in a male body.

This is different from a man cosplaying as a female character, which, I think most people would agree, does not actually count as being a woman.

The problem is that some people seem unable to conceive that biology could occasionally misregulate itself so badly as to generate a fairly typically female mind, with desire to be typically female, inside a male body. Well, tough. Biology is messy. Turns out it happens, and we have to deal with it.

You don't deal with it by dismissing the situation as a "man identifies as a woman". It's a little deeper than that would suggest. The statement contains as a premise that if you have the body morphology of a man, you are a man...when exactly what is in question is what to do in the case where cognition and body morphology don't match.