I think, although I have not worked this through enough to be sure, that the notion of gender identity has been mainstreamed from the medical literature because the concept of gender dysphoria cannot exist unless it is in opposition to something.
Hence, gender dysphoria - the feeling of being the wrong sex and unable to dress or function in the way traditionally asssociated with the other sex (aka gender) - can only exist if one assumes that the normal state of being is not feeling in the wrong body.
So how do you express this elusive thing that people who do not get clinically distressed about not being able to express themselves in the gendered presentation of the opposite sex and just get on with presenting as their own sex have? I mean, I just used a lot of words to explain what I mean.
Someone somewhere has come up with the concept of ‘gender identity’ to help describe the state of having/not having gender dysphoria.
Then two things happen.
Old school feminists say - we do not have a gender identity as gender is a social construct
Younger people (I generalise) say I do not have a masculine or feminine gender identity therefore I am non-binary.
Being non-binary is the state of not having or wanting to have a clear masculine or feminine presentation. Feminists have rejected gender so they don’t get the need to say one is non-binary - I think.
I need to prove this hypothesis by finding out the history of the concept of gender identity, but I will put money on it appearing in medical literature around gender dysphoria and not Pomoshire.