[benwad]

I feel like this has been said many times, but I'll say it again: there's a difference between sex and gender. Sex refers to the genitals you're born with, so you're correct when you say there are only two sexes (ignoring intersex for the moment, which does occur but can be considered an edge case).

Gender, on the other hand, refers to the social construct of how we see the relationship between these sexes in society. Transgender people are those who identify as a gender that doesn't specifically match their sex. There's no re-writing of science here, just an acceptance that a significant chunk of the population (yes, ~1% of the population is significant) want to live as a different gender than the one they're assigned at birth.

I hope that cleared it up.