That's all well and good, @Helleofabore, but unfortunately it's going to take some time to row back from where we now are.
I said in my previous reply to @StormingNorman that I don't believe a gender identity is something most people have. I guess without defining it, it's difficult to say whether most people have it or not. If I'm honest, I do feel that my biological sex is an identity of sorts. Certainly, I feel that having a body designed for pregnancy and childbirth has affected my identity, and did so well before I ever had children. But it is so inextricably linked to my sex, and not to clothes or hobbies or anything stereotypically feminine, that I don't see what it has to do with trans people. If I share any kind of identity with trans people, I'd be more likely to say I have that in common with Freddy McConnell than India Willoughby. So for me it is sexed, not gendered, even if Freddy McConnell doesn't agree that he shares any kind of identity with me.
I've focused so far on the impact of this on women. Even if dysphoria or lack thereof were an identity in itself, which I don't agree it is, a male person with dysphoria does not have the same identity as a female person without dysphoria. Or at least, not from the female person's point of view. And you cannot have a shared identity without the agreement of all the people concerned.
Where I think the concept of gender identity is really damaging is in terms of how it affects trans identifying people themselves, particularly this new demographic of adolescent females identifying as men or non binary.
I would say that as an adolescent girl (I have no experience of being an adolescent boy), feeling some sort of dysphoria in your developing body is more common than not. I certainly felt it as a teenager, and I was not autistic, did not have an eating disorder, had a happy home life etc. I was self conscious about my breasts and hips, wore baggy jeans and hoodies to hide my body, and would much rather have been one of the whippet thin skater girls who adopted a more androgynous style which just didn't suit my body at all. Who knows what might have happened if I'd grown up in an era where if you express discomfort with your female body and the expectations placed on you by a patriarchal, gendered society, people start suggesting you might be trans or non binary?
The whole idea that we all have a gender identity and that if you as a teenager feel uncomfortable with your body it might be because your gender identity doesn't match your sex strikes me as incredibly damaging and we really need to be moving away from this narrative. I will certainly be teaching my kids that a gender identity is something some people feel they have, like a religion, nothing more than that.