The whole situation is BS in the first place, back in the days the concept of gender was introduced to allow some flexibility in the social aspects while keeping sex (as in phenotype) a binary which science already knew it wasn’t. Bimodal distribution, yes, binary, no. Things get complicated fast once you go past egg cells and sperm, that’s the only actual binary that exists.

English in particular uses transsexual because back in the days activists wanted to avoid associations with sexuality, to not get tangled up in people’s homophobic sentiments. Other language use precisely that term, transsexual. Hirschfeld coined “transvestite”, back then a catch-all term for behaviour not conforming to your sex assigned at birth (and you could get a transvestite pass in Imperial Germany to stop the police harassing you for “inciting public disorder”), Benjamin coined “transsexual”, in English, as a diagnosis separate to “just liking to dress up differently”, it got replaced later on don’t ask me for a source right now.