If you go by social behavioral cues and personality traits, I am trans, or more specifically a woman with a penis.
Whereas others would argue that the only real difference is anatomy, and that social behaviors and personalities are flexible and fluctuate.
That seems to be what the argument is about. What is the actual definition of a “man” and a “woman?”
But if you go by social/behavioral traits, any powerful women could be potentially be classified as a man because they don’t display the traditional social and behaviors and traits of a woman, even though they very much consider themselves a woman. I know a lot of women who would consider such a notion as being sexist, stereotypical, and insulting.
And then you have the problem that these things change over time. In some cultures of the past, men used to wear dresses and have long hair. Now in most of the western world it is the opposite. The term “gentleman” originally came from the fact that these “gentle men” were considered to be more feminine than normal men. Women uses to stay home and make babies and take care of the home. Now they are workers and CEOs of companies. Times change.
I think it would be hard to get everyone to agree on which specific behaviors or traits correspond to “man” or “women,” especially considering how much they change over time.