I think a lot of men derive a fair bit of their self esteem imagining themselves better than women, by whatever measurement. Usually those who have little achievement of their own apart from the accident of birth as males.

I have proof that people give a damn (see links below). Just because you don’t give a damn, don’t assume others don’t.

Can women run faster than men?
See Jane Run. See Her Run Faster and Faster.
Do men run faster then women?
Who runs faster, MEN OR WOMEN???
Women of the Future Are On Track to Run Faster Than Men
Women may run faster than men in 150 years’ time
when will women overtake men?
Men are faster than women – but does that mean bets should always be placed on colts?

I stopped after the first two pages of Google results, but the links go on and on.

Men do, on average, beat women in physical strenght. What the hell do you care though? Nobody gives a damn who runs faster than who.

As you say, if biology makes men such that they are Y and women such that they are X, then there would be no need to tell men to be Y and women to be X.

I always find it sadly funny when people argue that women (or men) should be a certain way because “that is the way they are.” This is not only circular, but also silly.