Except that most people have an inherent sense of their own gender.

You seem to think that being put in a box and jumping into a box are the same thing.

(You also do not fully understand the way queer is used, you're only talking about genderqueer, which is a subset of being queer).

Gender labels are inherent. It's what they mean that is and has to be fluid.

To a trans woman, being a woman is vitally important. Not being recognized as one is a battle she goes through constantly. Same for a trans man. Same for somebody with a non-binary gender.

It's not a battle cis people can fully understand. Saying nobody gets to be a woman does not solve it.

Again, being put in a box is different from jumping in one. Ask any cat.