I think it is closer to the truth to say that gender is a social construct in the same way language is a social construct. The Universal Grammar Theory[0], pioneered by Noam Chomsky, gives evidence that language arises from a biological predisposition that is cross-cultural. The social construct arises from the biological construct.

0. https://en.wikipedia.org/wiki/Universal_grammar

This is another example of people redefining words then claiming other people are unenlightened because they use the original meaning and not the redefinition.

Gender has been used as a synonym for sex for a long time. Merriam-Webster and The Free Dictionary list that meaning before the more recent meaning.

You're simply wrong to claim the way you use the word is the only way it can be used.

Those words are used interchangeably in modern discourse. But it's not like the craziness goes away if you define the terms more carefully. There are people who seriously beleive there is no biological difference between the sexes when it comes to internal characteristics like mind and personality. The external differences are, I hope, obvious to all with eyes to see.