I think if a whole bunch of people who are unequivocally female bodied on this thread can't agree on a common experience of a "female brain", there can be very little credibility for a man thinking he is experiencing a "female brain".
It's telling that there are no people out there insisting they were "born the wrong height" or "born with the wrong size hands". Indeed, at various stages in the womb the foetus has no legs, no lungs etc, and yet no one is claiming they have a brain that got stuck without legs. It's only the sex divide when the body seems to have this side effect of sometimes generating the wrong brain, and the sex divide just so happens to be one of the most socially and psychologically significant in our society, the one on which culture (mostly patriarchal) has layered a whole load of bullshit about how men and women differ in ways beyond the body, mostly to do with men's fascination with women's role in childbirth and sex and their retro-fitting stories to make sense of something they don't actually know about, and one in which the divide still has significant impacts in how we live and are seen socially.
The brain grows out of the body. The mind is just the consciousness of the body. They are not two separate things, they are parts of one thing. Even if there are certain physiological factors more common in one sex than the other, finding them in members of the opposite sex doesn't mean "Oh that's a female brain in a man's body", it means some men also have those factors and therefore those factors are not exclusively female. Finding them in a man just means you found them in a man. It in no way means that man is somehow a little closer to being a woman than other men.
If you think all squares are red and all triangles are blue then one day you find a red triangle, the logical response is "oh some triangles are red" not "oh all this time we've been wrong thinking a square is a shape with with four equal sides, some squares look like triangles but are actually squares"
The genderist belief that a brain could somehow be "meant" for a different body, somehow "know" it's supposed to be in a different body to the degree it expects to look down and see boobs or whatever, yet still be capable of handling its actual body including all the sex-specific parts of that body makes no sense at all.
All that phrase can ever mean is "I think my personality is more like what I think the opposite sex is like than what I think my own sex is like" and that is nothing more than one person's projected sexism.