David Reimer is an ugly botched experiment, that adds nothing to this discussion.

“gender roles have at least a biological explanation (beyond the social construct which, indeed, creates those stereotypes”

Roles are constructed, and biology seeks to statistically reinforce such roles.

“In other words: in 90% of the cases at least, a ‘boy’ will feel to be a ‘boy’, and a ‘girl’ will feel to be a ‘girl’, and both will experience a difference between their identity and the identity of the opposite gender.”

The brain isn’t of a sex or gender, as the dimorphism of the brain is not a difference of distinct types, but of degree. One’s brain may have a relatively high degree of empathy and relatively low degree of aggression, and this is simply to improve the likelihood that the individual will come to be more affiliated with soft, nurturing, “feminine” associations. In turn these associations are associated with females, and one associates oneself as being like a female, of “being” a female. As Judith Butler says, “There is no gender identity behind the expressions of gender; … identity is performatively constituted by the very “expressions” that are said to be its results.”

At the ultimate level, of course you’re right. The point here is not to discuss deep philosophical meanings of what exists and what doesn’t exist. Gender might not exist, but our heteronormative cisgender society is based on the assumption that at least two main gender roles exist, and that such gender roles have at least a biological explanation (beyond the social construct which, indeed, creates those stereotypes). That is, while it is considered that certain biological markers during the development stage of the embryo will indeed create a difference (in at least 90% of all cases) between ‘genders’ (and this has been experimentally proven — look up the David Reimer case, showing that gender identity is not merely social conditioning), that, by itself, doesn’t mean that persons automatically will adhere to society’s stereotypes — that is socially and educationally conditioned.

In other words: in 90% of the cases at least, a ‘boy’ will feel to be a ‘boy’, and a ‘girl’ will feel to be a ‘girl’, and both will experience a difference between their identity and the identity of the opposite gender. That is gender identity; it is very likely fixed at birth (although we still need much more research on those biological markers which apparently define gender); and it’s a strong conviction that we will carry with us — as strong as the conviction that we’re ‘human beings’ and different from cats and dogs, for example.

The other thing is saying, ‘because I’m a boy I will dress in blue and wear trousers’. That is gender presentation or expression, and it’s fully socially conditioned, being modeled after the current society’s gender stereotypes. Such stereotypes obviously change with time and location. So we cannot say that gender presentation is somehow tied to any biological structures (or we would still be dressing like we did when the human species was hunter-gatherers)! In that regard, yes, ‘gender presentation’ does not ‘exist’ in the sense that it is a social construct. Gender identity is correlated (in 90% of the cases) with gender presentation, but it’s a completely different thing; like sexual orientation, it’s very likely tied to certain structures in the brain. In other words: no matter what the year or the place or how weird a society’s norms and stereotypes might be, a ‘boy’ will feel like a ‘boy’ and wish to identify with members of his own ‘gender’, adopting their stereotypes; and conversely for ‘girls’ too.

There can be a society with ‘genderless presentation’, i.e. all members of that society will present themselves in exactly the same way. I would also claim that such a society would end all discrimination — since everybody would dress and behave exactly in the same way, have the same jobs, and so forth. Nevertheless, even if the gender presentation in such a society would be the same for both main genders (and all others in the spectrum), 90% of the ‘males’ would still identify with the male gender, while 90% of the ‘females’ would identify with the female gender, even if externally they would dress and behave in exactly the same way. I would claim that in the 1980s we were quite close to that utopian dream, as the youth would dress in sloppy T-shirts and jeans with sneakers, and both genders would wear their hair short, and girls would refuse to wear makeup. The external presentation of both genders was really quite close, and tomboyish girls were much more accepted back then than they are today. This is a good example to show that an utopian society where gender presentation does not differ between the genders is almost possible.

Interestingly enough, in the 1990s gender presentation started to change again, to create a larger rift between the genders. I haven’t read any sociological studies attempting to explain that phenomenon, but it would be very interesting to understand why that happened.