There's more variation of height within male and female groups than between groups, but still you can confidently say that on average males are taller; so "far more variation within the group" doesn't say much

> can't blame our lack of cognitive empathy on biology, it's probably pure socialization/education

Any evidence?

A study linked from one of your links says: "Our study demonstrates that, although there are sex/gender differences in the brain, human brains do not belong to one of two distinct categories: male brain/female brain."

So it looks like there are, actually, differences.

Also, it is kind of assumed that we need more cognitive empathy; but why exactly, and how much is too much?