> It's not a sex characteristic, it's a gender characteristic.

They're one and the same.

> But denying the idea that humans have both characteristics derived from biology (sex) and from societal expectations (gender) is simply objectively incorrect.

I don't deny the existence of social expectations (you severely misread what I wrote), but those expectations were deriving from the recognition of the objective truth of one's sex. They were never a matter of one's "internal feelings", they were an extension of one's sex.