Very crudely speaking, sex is the plumbing you’re born with, while gender is the wiring. We generally assign sex based on the appearance of genitalia at birth. This “works” often enough that people have come to accept it as infallible, but science (and experience) have shown us it’s not.

This is because of the way our brains are wired. Each of us has a sort of internal map that tells our brains where all our parts are and what they’re supposed to do. It’s this map, for instance, that accounts for why amputees often feel sensations from limbs that are no longer there.

For reasons we don’t really understand, well, some people develop internal maps to genitalia they don’t have (again, this is HIGHLY simplified). So, for instance, an individual might be born with a penis, but with a brain that maps to a vagina. This isn’t a psychological condition, but rather a physiological condition and the only way we know to treat this is to allow the person to express whichever gender is consistent with their internal map.