Not really. Sex is more of a spectrum than an absolute. Shades of gray, rather than absolutely black and absolutely white. Men and women each have varying levels of testosterone and estrogen. It isn't that men only have testosterone or that women have only estrogen. Then it is further complicated by hormone receptors and expressions.
By "binary" do you mean completely one or completely the other? This or that, not bits of both?
I believe the expression is that "gender is a social construct" not "sex". Would you go as far as that, gender instead of sex?
Yeah, I pretty sure that is what I said. Are you too stubborn to agree?
Social terms tend to be more vague and nebulous than scientific terms. Some people can deal with ambiguity more easily than others who need certainty.
You are under no obligation to acknowledge anything. However, I find it helpful in this life to understand something before dismissing it out of hand - especially bothersome things.
Yes, that's the problem with excepting transgendered people.