The whole inner identity is a fiction. It is loosely based on stereotypes of how biologically different people behave, but it is meaningless.

It's even worse than that, I think. In most case, "gender identity" is entirely based on sexist stereotypes of how the two sexes appear, and only to a much lesser extent on stereotypes of how they two sexes behave.

Most males who ID as the opposite sex are very selective about which behaviors associated with the female sex they emulate - they equate "acting like a woman" with being submissive, coquettish, slutty, slavish to male sexual desires, giggling, being dumb, pretty, delicate, physically weak, helpless, squeamish, useless around mechanical things like cars and power tools - and those are the only types of behaviors they try to emulate. When it come to wiping other people's asses and noses, scrubbing the toilet, washing the dishes, cleaning the house, making sure everyone is fed, doing laundry, working crap jobs, always thinking about other people's welfare, putting other people's feelings and needs first, being self-effacing, swallowing their anger, biting their tongues, not getting their own needs met, not being listened to, being excluded from various spheres, being passed over for jobs and promotions, never getting a chance to realize their ambitions and pursue their dreams, accepting unfairness and discrimination as "one's lot in life" and putting up with it without a word of complaint - not so much. Not at all, in fact.

In my observation, the vast majority of stereotyped behaviors that female people are socialized to engage in are behaviors most males who "identify as" girls and women have absolutely zero interest in adopting.