I'm not sure it's so bizarre when you think about it. First, though, I want to clarify that I'm not saying that no men support the practice, or that no men apply any kind of pressure. However, it's at least as often the case that women are the ones who perpetuate the practice without any interference from men. The reason for this is that it's simply become tradition. People have gone along with plenty of practices which are deleterious to themselves because those practices were traditional, and even in the absence of any pressure.
See, for example:
Female Genital Mutilation On The Decline, But Still Too Common : Shots - Health News : NPR
BBC News - Newsnight - Female genital mutilation rife in Egypt despite ban
Women
Interesting quote from the second link:
This accords with my understanding of the issue.
Some interesting findings from the third link, which summarizes the findings of a broad survey of Egyptian Women on the subject of female genital mutilation:
The vast majority of women in Egypt support continuation of the practice.
Those that don't tend to be better educated, and, presumably, are more likely to be aware of the negative consequences of the practice.
Mosques are apparently treating the practice in a negative light.
It's worth noting that female genital mutilation was banned in Egypt in 2008 by a predominantly male legislature.