Do you think the binary gender system of male vs. female is natural, socially constructed or both?

Do you think the binary gender system of male vs. female is natural, socially constructed or both? And why?
Could we construct a very different gender system, i.e., 3 or 4 or 5 genders, that would also work?
What would happen if we stopped labeling people in terms of gender entirely?
Edit for errors and conciseness

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