Seeing gender as a social construct is a Postmodern theory. Seeing gender as a biological fact is Modern objective theory. Modernity tries to flatten the whole world into objective 'science', while Postmodernity tries to flatten the world down into social constructions. You can try to say it is both 'nature and nurture' but this just creates cognitive dissonance.

More importantly what type of value system do you want to have? Do you want to believe objective truth is more important, or do you want to believe living in a just society is more important? You can't have it both ways.