Sex is not a social construct and I never said it was however gender is. Gender may have associations with certain biological traits but the nature of gender, is socially constructed. Also there are societies where there are more than 2 genders. The traits and expectations associated with each, the way we define them is socially constructed.
We associate Manhood with male genetalia. But what does it mean to be a man? That question is very dependent upon cultural expectations and the way people define it.
Who's the most manly out of this group?
Also in our culture we still have an expectation of submissiveness from females. Many argue that this is biological but it is social. In other parts of the world women are the sole decision makers or the holders of status and land.
In a similar fashion Race, while most often tied to skin color or a few other traits, has little biological basis. The way define people by race is socially constructed and yet has a profound impact on identity and reality people live in.