Gender identity should exist first and foremost because people identify their genders.
So identities exist due to that which identity is based from.
All things should exist by their cause.
All identities exist based on the existence of a thing.
A thing called gender exists and is therefore identified so genders should be identified like a container of water should be hot if the temperature of 100 degrees exists in it and of course the number is identified so forth and so on.
That's the first thing in regards to ontology and teleology.
Second point, gender identity should exist is due to social and legal climate.
Just like voting rights for women should exist due to social and legal climate.
All lobbying, petitioning, rallying and protests should cause the effect of what it does which is why protestors do what they do with the information of what SHOULD be done to bring about what SHOULD happen.
The opposite side can argue the basis what should be.
However the basis won't exist being that genders exist already.
Let me respond to some things the opposite side has stated.
"gender roling is just a category that aims since the dawn of time the segregation of specific groups based on the physical capacity."
Gender roles have been established by their nature like light and the dark .
The lightness and the darkness have categorize themselves innately. We recognize the ontology and communicate it in language.
"it's useless to have categories that only aim to divide and harm ourselves"
Ok well having female and male categories divide that which is the truth in benefiting us such as what each can only do and may have to aid to the other in deficiency.
So it works and is useful by the perspective taken.