Gender is not a social construct. Your gender is the ability to become pregnant or to impregnate someone. This statement is not about politics, its just mere biology.
What's socially constructed is how your gender is presented or implied because of said society. No matter how society "constructs" your gender, you're still biologically male or female.
Even with gender reassignment surgery - your'e still biologically male or female, its just that the "presentation" of your organs have been surgically altered.