I was thinking about this while driving to Ikea, and indeed it doesn't make any sense when you unpack it.
I'm a woman because my body is female. It doesn't matter whether I'm happy about that or not, it's the way it is. It's the same as observing that I'm white, and I'm 170 cm tall and I take a size 37 in shoes. The way I think about myself and the way I operate in society is informed by all of these things, because my body is me and that's what my body is like.
What if I insisited that I was "really" 185 cm? And I insisted you had to treat me as if I was 185 cm? How would that work? Maybe you'd talk over the top of my head, you could do that. Maybe I'd get all huffy if you laughed at me for wearing clothes that were way too big for me, but I'm sure you could manage not to do that. But if you were in charge of a ride where the minimum height was 180 cm, should you let me on?
I don't know what it's like to be 185 cm, or to have size 42 feet, or to be black, because I'm none of these things. I might imagine I knew, but it would only be my imagination because I have no experience of actually being that way, nor can I have. I don't see how believing you're the opposite sex is any different.
You like frilly blouses and makeup and high heels and nail varnish? News flash, that just means that you like frilly blouses and makeup and high heels and nail varnish. Lots of women don't. They're still women. Some men do like these things, they're still men.
I don't know what else there is. There is no "essence of womanhood" that is separate from actually living in a body that is female, just as there is no essence of height that is separate from living in a body that's a certain height. Liking things you perceive are popular with taller or shorter people doesn't make you a different height. Liking things you perceive are popular with women doesn't make you a woman.
Absolutely everything anyone has ever claimed as "evidence" that they were allegedly born in the wrong body, or are in some way "really" a woman, boils down either to this nonexistent "essence of womanhood" or to the regressive gender stereotypes of categorising women as people who behave in a certain way or like certain things.
Women would rather like to get away from these stereotypes, where they're not expected automatically to be kind, caring, nurturing, passive, to put men first, to like dressing up in a certain way and to have certain colour or other preferences. They'd like to be themselves, as they are, and particularly not to be criticised for being themselves in a way that would not be criticised in a man. (We're back to an assertive girl is bossy but an assertive boy is the boss.)
Gender ideology is the most regressive, stereotyping thing there is. It couldn't exist without these restrictive boundaries society imposes on females (and males, come to that - big boys do cry). The sooner everyone is free to have whatever personality and preferences they like without being judged and pigeon-holed because of them, the better.
ETA: Not that long ago, in Britain, a woman politician was asked to define "woman". She came out with a load of sexist, regressinve crap about a woman being someone who is kind, caring, nurturing, blah blah blah. Do I even have to point out the ridiculousness of that? What about women who aren't these things? Are they men? What about men who are - and thankfully despite this woman's idiotic outlook, very many men are. Should we change all their birth certificates to say they were born as girls? And then there's the delicious irony that very many transwomen appear to be none of these things.