Thing is, there’s only really something to be gained if you identify into a group who are less privileged than yourself. For eg, a white man identifies as a black man, only everybody can see he’s a white man so he won’t suffer the racism a visibly black man would. The only time his identification as black will make any difference is if he’s going for a position which has been reserved for a POC.
Conversely, me for eg. I have a very obvious disability which prevents me from doing lots of things that people who don’t have that disability can do easily. There’s no point whatsoever of me identifying as not having that disability because I’ll still have it, it’ll still be obvious and I still won’t be able to do all those things people who don’t have that disability can do.
So, a man who identifies as a woman will still be a man. People will know he’s still a man because hardly any men truly pass as women, not even the ones who’ve had all the surgery and hormones, so he’ll still be treated like a man. Not only that but he’ll still have the socialisation and expectations of a person who was born and raised mail, and who has all of the advantages afforded to him that brings. The only real difference will come when he wants to access spaces and positions reserved for women. Conversely, a woman who identifies as a man is still a woman. Granted transmen pass better than transwomen if they’ve had surgery and hormones but in most cases people can still tell. I for example could transition, but I’m 5 feet 2 and proportionate for a woman of my size, and given that most women are smaller than most men, people will still be in most cases able to tell. In the world of men she’ll still have the socialisation and expectations of a person born and raised female, and will be subjected to the disadvantages that brings, and when she tries to access positions currently reserved for or favoured for men she’ll lose out, because sexism.
Interestingly the GRA has an exception whereby a women who transition to be a man will not be eligible to inherit certain land and titles, because of sexism.
So, in short, self identification is a way to have your larger slice of the pie, then eat some other less privileged person’s slice as well, because for the less privileged person it doesn’t work.