Transgender

For most of modern history, scientists, doctors and judges have agreed that humans can change sex – they just haven’t agreed on how it can be accomplished.

Not only in modern society, by the way. Take this as no more than a funny anecdote if you wish, cause I can't provide a source, but:
My cousin lived among a native tribe in Panama for a while.
Traditionally, they only allowed men to hold political power (by speaking in the common assembly), but they only allowed women to inherit and own property.
This serves as a method to separate wealth from power, and gives women considerable status in society.
But it also poses a problem: When a couple doesn't have daughters, they can't hand down their wealth to the next generation.
The way around this was simple: If there were no daughters, the youngest son would become a daughter.
He (or rather, she) would lose the right to speak in the assembly, gain the right to inherit, wear the traditional women's garb and be 100% socially female, while being 100% biologically male.

I'm not saying this is a good thing, especially as their opinion doesn't seem to matter all that much. But it shows that gender roles are not based on nature at all. They're different in every society.
And natural sex is more than complicated enough as it is.