Since equality 'never' happens in nature; either men must understand women better than women understand men; or else women understand men better than men understand women – on average.
(Or, the difference could be too small to make a difference, except perhaps at the extremes.)
So which is it?
I would say the answer is obvious: men understand women better than vice versa!
More exactly, over time most men learn to understand women better and better; but women instead learn to tolerate that which they do not ever understand.
Why? Perhaps because biologically men court and women choose; so men are in surplus and women a shortage; therefore a man typically wants and needs to understand women, so that a women will mate with him and raise his offspring (because if she doesn't, they will all die - so mating is only a first step).
(There may also be more existential reasons why men are more motivated to understand 'reality'.)
But a woman (a young healthy woman, anyway) is intrinsically in-demand, and doesn’t really need to understand men – just to pick the best one available…
Cross posted from jrganymede.com/2017/05/19/do-men-understand-women-better-than-women-understand-men - where there are some comments.