One of the primary challenges of explaining the rules of attraction to the opposite sex is that both sides have a natural tendency to project their own attraction factors to the other one. So, men can't figure out why women aren't attracted to loyalty, responsibility, and sexual purity while women can't figure out why men aren't attracted to university degrees, good jobs, and intelligence. This last matter is one of particular importance to a certain group of women, as women who identify themselves as intelligent find it especially difficult to grasp that what they consider their primary attribute, and what they tend to find tremendously attractive in men, is of relatively little value to men as an initial attractant.
As I have previously pointed out, the fact that nearly all women are attracted to smarter men and desire them as mates does not mean that most men feel that way. This should be obvious, and it is a very good thing too, otherwise it would be almost impossible for men and women to pair off. After all, both sides of the couple can't be the smarter one any more than they can both be the taller one. Most women understand that dumb men aren't attracted smart women - such men feel "threatened" is the usual line - and they aren't concerned about that because, being hypergamous, they usually aren't attracted to less intelligent men. What they don't understand, unfortunately, is that most intelligent men aren't attracted to their intelligence either.
That doesn't mean that smart men don't value female intelligence in a relationship, only that they tend to do so in the way that a woman values loyalty in a man. But it means that men don't, by and large, find themselves instinctively drawn to displays of female intelligence in the same way they are drawn to displays of large breasts, well-formed posteriors, or long hair.
But even when female intelligence is valued, the value isn't necessarily what the average smart women thinks it might be. This is because intelligence, like height, is relative, and +1SD is +1 SD. The "smart" 120 IQ girl looks even dumber to the 150 IQ guy than the "dumb" 95 IQ girl does to the "smart" girl. And once the intelligence gap passes a standard deviation, it can be difficult to distinguish between the various stupidities being expressed, so for the highly intelligent man, it doesn't much matter if she's got an IQ of 85 or 135, because it all looks pretty much the same to him. The lower IQ may even be preferred by some men, since intelligent women tend to be much less agreeable and more prone to instigating verbal conflict than their less intelligent sisters. One is unlikely to see a woman with an IQ below 116 launching into a pedantic fighting withdrawal every time she is caught saying something materially false, just to give one example.
Height is a useful proxy here. If you're Shaq, can you even tell at first glance if a woman is 5'2"or 5'8"? Does it really make any difference to you? Then consider that to a man with the lowest possible Mensa score of 132, a woman with an average IQ of 100 is proportionately to him what a 5'4" woman is to the 7'1" Shaq. It's even worse at the so-called genius level of 145 IQ; the average woman looks proportionately like a 4 foot-something midget. For most tall men, anyone below a certain height is simply "short". And for most intelligent men, anyone below a certain level of intelligence is simply... let's just say "ünfiver".
However, there is one area where intelligent men tend to value female intelligence, namely, their offspring. Very few smart men can bear the idea that their children might be grinning idiots incapable of any intelligent discourse with them. However, note that children are an intrinsically LTR-related subject, which shows why attempting to use one's intelligence to initially attract a man in an STR context is a basic category error. It no more works for a woman to attempt to attract a man by displaying her ability to bear him smart children than for a man to attempt to attract a woman by displaying his agreeability as well as the high probability that he will always remember her birthday and the correct toilet seat position.
So, female intelligence does have an appeal to the sort of men that smart women want, but it has to be utilized correctly, and in the proper context. (Of course, this is also true of the appeal of male intelligence to women, but we'll save that for a future post.) The key thing to remember is the vital distinction between I (initial attraction) factors and R (relationship) factors. For men who value it, intelligence is almost always an R factor, not an I factor.