Earlier quoted context omitted.
If someone said "you're a woman", would you disagree?
Only on the basis of everyone until that person having said differently, up to and including someone else already having defined “man” as a male human.
Even within the bounds of a gender (e.g. masculine), people will find themselves wanting to be seen as a particular point within that gender's spectrum. (E.g. you might want to be seen as a tough guy, or a sensitive man, etc.) It can be frustrating to feel like you are the tough guy but no one seems to treat you that way.
The point is that experience is different for different people. Many people are comfortable with whatever, others aren't and want to try to take deliberate actions to make themselves be perceived more like how they see themselves.