How Can There Still Be a Sex Difference, Even When There Is No Sex Difference?

Intuitively it made much sense for me when I was in high school and trying to figure out the world.

People perceive high, even extreme intelligence as some beneficial trait, but I don't think that's how we should look at things. Evolution does not care about men as much as it does about women. Man can be far from being best fit for raising children and still forward his genes to next generation. Women need to be much more optimized, stable. Too high or too low intelligence is a neurological flaw in men that makes them worse parents from evolutionary perspective but they can get away with it. Women can't.

It might change after many generations of society that takes care of children of deranged or disinterested mothers. Having extra copy of X chromosome sure does help with stability but there are many examples in biology where simple obvious mechanism are overruled by special contraptions forced by evolution to result in the opposite of what simple logic would dictate.

For an even more "untouchable" subject try: https://en.wikipedia.org/wiki/Race_and_intelligence

It uses standardized test scores. I quote findings below. Remarks inside parentheses are mine.

"The third column in table S1, reports the estimated male/female variance ratios with standard errors in parentheses. In all but five countries (There are 41 countries) we can reject the hypothesis that the variance ratio is equal to one at 5% level. In all the countries where this hypothesis is rejected, the variance ratios are larger than one indicating that the male variance in reading is higher than the female variance."

In other words, male variance > female variance with 95% significance level in 36 countries, and no statistically significant difference in 5 countries. There is no countries where female variance > male variance with statistical significance.

There are various interpretations of this result. The usual interpretation is that there is a sex difference in variability. Another interpretation is that since variability difference is not universal (in 5 countries it is not statistically significant), variability difference is cultural. The later interpretation is argued in PNAS paper cited below.