Even though there are only two sex chromosomes, issues with them can cause people who are physically intersex.
Then there's all the complexity of the sense of self. Some people could feel they have the 'wrong' body and be fine with that. Some can't.
-Heterosexual male tired of oversimplifications
It is completely different if it is a physical disorder, but this is not the case in vast majority of cases.
Also: if a identity or an emotion is real to me, does it not become real through that act itself?
Sometimes this will be through believing he has a "female brain" in a male body. Or perhaps he might think he's "born in the wrong body". Or maybe he'll start to believe that being a woman or a man is based on some internal "gender identity" of which he has the female type. Sometimes this is given a spiritual aspect, like a female soul.
If he takes drugs to suppress testosterone and boost estrogen, he may start to believe that he is no longer of the male sex but is becoming female. Even more so if he elects to have surgery to remove his testicles and fashion his penis and scrotum into a non-functional cosmetic simulacrum of the female external sex organs. Some of these males even start to believe they're having a menstrual cycle, despite lacking any anatomy involved in this process.
However he reaches these conclusions about himself, every single one of these beliefs is false. These are delusions.
I see no proof of these assumptions. How humans see each other and themselves is not primarily chosen by their unchangeable (save medical interventions) organs but by how we are read by our peers. We are not talking about a purely biological problem, but a social one. Humanity has, for the longest time being, assigned fixed profiles to these readings, which luckily has started to break up in the last decades. Now of course each individual is free to base parts of their own identity on their unchangeable biological traits, and you also are free to do so, but that does no generalize to the whole population. Humans should be free to base their identity to their own liking.
This can lead to some cases which do not make sense like your "male menstrual cycle" example, granted. These anecdotes however as well do not generalize towards the initial claim of the other user and the first assumption.