Men are more intelligent than women (and women are more beautiful than men)

In all societies, intelligence can be an advantage for men because a more intelligent man has a greater ability to acquire status which enables him to attract more women and thus have more children. This status can be acquired by various means, such as strength, influence, wealth, etc. So for a man, more status means more fertility.

Since in the mating game it is women who choose men and not the other way around, the question of whether a man would prefer beauty or intelligence in a woman is somewhat beside the point. Also, since the game of life is about reproduction and not about intelligence nor beauty, a man would prefer beauty which correlates with fertility in women. Just as how women would prefer intelligence which correlates with fertility in men (but also beauty which is an indicator of intelligence in men). Which is not to say that intelligence is completely useless in a woman (because his sons would gain a reproductive advantage from his wife's intelligence genes), but intelligence is not an indicator of fertility in women (in fact it is the opposite).

Since the supply of women have always been less than demand, there has always been less evolutionary pressure on women to excel than on men. A woman has to literally do nothing to attract a man (she didn't have to be devious or clever in attracting a man), she has no real use for intelligence. Beauty on the other hand would give her an advantage in attracting men with status.

But then why did intelligence in women evolve at all? Since the more intelligent men were more likely to be successful in mating with women and having more offspring, children (both boys and girls) in the second generation inherited those intelligence genes from their fathers. These girls in the second generation, while being more intelligent (and numerous) than other girls who were the offspring of less intelligent men, nevertheless had no mating advantage over their less intelligent cousins. But a more intelligent man would have more luck with these second generation women than a less intelligent man would have with these women. So in the third generation as well, boys and girls possessing more intelligence would be more numerous.

So it seems that women's intelligence has always been dragged up by the men they mated with. And of course male beauty has always been dragged up by the females they mated with.