Contrary to the top answers, throughout human history, “high levels of intelligence” in men has been an undesirable trait for sexual selection…
In prehistoric times, where our sexual behaviours still very much originate, men were generally hunter/gatherer types. Whilst women were heavily protected in central society to ensure the continuity of our species. The reason for this, in part, is due to the fact that women are born hypoagent, whilst men are hyperagent. This is precisely why the law of attraction, for most species, assigns males the role of “competitor" and females the role of “selector". Since the very beginnings of humanity, sexual selection powers have lied very much in the firm grip of females. Females have “Hypergamous” instincts, which means they target their sexual preferences towards the highest status available men (in relation to the social hierarchy). Beyond that, women also all share the same intrinsic value as “breeders”. This is how they were able to assume a state of protection in prehistoric villages and how they adopted evolutionary functions such as ‘automatic own group preference’. However, males remained largely expendable to women and other males. In these times men could be taken down a valley and beaten to a bloody pulp for even challenging a woman.
To answer your question, the reason “intelligence” is undesirable, is due to a females need to outsource risk to a man (so that it might be easier for her in undertaking pregnancy and motherhood). This requires attraction to a trait called the “Willingness to Emote”. The “Willingness to Emote” is found, to a greater extent, in men with lower levels of intelligence. On the other hand, in a prehistoric environment, higher levels of intelligence were associated primarily with the trait “Introspection”. This essentially means ‘thinking before you act’ to reduce risk. It is therefore much easier to outsource risks and provision to a less intelligent man who will 'act before they think'. Women are the proprietors of sexual selection and have assumed this power through a biological function known as “automatic own group preference “. This means they prefer to associate with other women socially, and adhere to ideas that primarily serve women above men. On the other hand, men’s natural instincts include the protection of women and provision of security.
In summary, “intelligence” is not a sexually desirable trait, because through sexual selection women are aiming to achieve maximum benefit. They achieve this by exploiting the “willingness to emote” (acting without thinking), and social status (material wealth) of men. The top answer, which indeed was very feminist suggested that “feminist views” helps a man to be attractive. Though I agree that men holding feminist views is not especially “intelligent” of them. On the contrary, its men who could plausibly display a logical opposition to feminism that women would inevitably remove from the selection process.
Essentially, a woman will not typically select a man who has autonomy over his own beliefs regarding women. Or is intelligent enough to avoid the manipulation of their carnal instincts in the favour of female interest. Intelligent men ARE NOT attractive to women per se. Rather intelligent men, with high status and willingness to being manipulated into taking on additional risks on behalf of a woman, ARE. This is fundamental human evolutionary theory. Without an ability to provide for a woman, a man becomes too easily expendable to justify as a long term option. More simply put, in the absence of “willingness to emote", intelligence becomes undesirable.