The reason "men identifying as women" isn't a correct description of transgender women is because "men" and "women" can't have two simultaneous definitions in that sentence. It adds confusion and is essentially a dog-whistle for educated bigots while also incorrectly portraying it as a sort of paradox so simple minded or uneducated bigots can feel like it's some sort of obvious contradiction that libruls are too dumb to realize.
You're using "men" to describe gender-assigned-at-birth and you're using "women" in the context of our modern scientific understanding of gender identity. Either you accept contemporary science and so they're not "men" doing the identifying, or you reject modern scientific understanding and conclude that it's just some silly men that think they're women and what next they'll identity as trees lol what if I identify as a billionaire lol.
oh my flipping gosh this is so hilarious I'm laughing so much why hasn't anyone thought of this before like what lol what haha what's next I can be a helicopter? I'm a helicopter because I said so! Oh my flipping gosh man you're something else you should write this down and share it with the world