Sure. I don't understand the competition argument though. In my HS and College years it did not matter if the top student was a man or a women, it just mattered if it was you or someone else. And as far as I recall men and women were fairly evenly matched. Why do you think they should compete separately?
I had to think about this. As a heterosexual, I want to say chemistry.
(Others have brought to non binary individuals but I have to confess that I can’t make assumptions about their dynamics.)
Sometimes I feel the same way with problem solving as I do when I am attracted to a person. It makes me wonder if competition and inter personal romantic chemistry are related wrt how our brain perceives it.
And there is limited/fixed mental bandwidth that we can only focus on one at a time? Just wool gathering..off the top of my head. What do you think?