Society has everything to do with gender roles, which are assigned according to one's apparent gender. Society has evolved to the point where I can do any job a man can, [in theory] as long as I'm capable, but not to the point where I can say I actually am a man, inside, and be accepted. But what if that part [the biology] is just one of the many things we haven't learned yet about the human body and brain?
Because we don't know it all, nor even close to it.
Maybe transgenderism is a psyche disorder, but those who insist it isn't, call it "dressing up" and "disgusting" are proceeding from an emotional place, not a knowledgeable one.