In cross cultural studies, a consistent finding is that women are primarily responsible for suppressing the sexuality of other women. One of the main reasons for this is the use of sex in cultural contracts with men to negotiate provisions of food, protection, and wealth for women.
The more expensive that sex is for men, the more that women benefit from their interactions with men.
This has resulted in complex rituals where older women (often described as "matriarchs") work together to suppress the sexuality of younger, more sexually active women.
In modern societies this occurs through slut shaming. Which is primarily perpetuated by mothers and by female peer groups.
In hunter gatherer societies it occurs through rituals surrounding a woman's first period. Again this is almost exclusively done by the mother and by other women, with the primary purpose being to preemptively remove her from the "dating pool" for men.
And it also occurs in societies that practice female genital mutilation. Where the primary purpose is to decrease a woman's sexual desire and therefore her willingness to engage in sex with men.
The view that men suppress female sexuality received hardly any support and is flatly contradicted by some findings. Instead, the evidence favors the view that women have worked to stifle each other's sexuality because sex is a limited resource that women use to negotiate with men, and scarcity gives women an advantage.
Baumeister, R. F., & Twenge, J. M. (2002). Cultural suppression of female sexuality. Review of General Psychology, 6(2), 166-203.
FGM is just the most extreme version of this practice. It is almost universally performed by women, and is often objected to by men in those same societies. Usually on the grounds that uncircumcised women make for better sexual partners.
Some of this research in quoted in the book The Empress Is Naked.
In their paper, Baumeister and Twenge cite numerous studies and evidence that suggest so. “The decision about whether and when a particular girl will receive the operation is made by her mother or grandmother”. Men in Islamic African countries not only accept to marry uncircumcised women, but in fact they prefer it. They consider European women very desirable for wives, “because the men found the European women (who had not had genital surgery) enjoyed sex more. These findings are directly contrary to the theory that African men prefer women whose sexuality has been stifled by surgical methods.” An interesting study in Sudan questioned 300 men who had two or more wives, one of whom had had the operation while the other had not. “Nearly all of the men reported that they preferred the wife who had not had the genital surgery.”
There is a social dynamic developing around FGM in African countries, that parallels that of slut shaming in the West: women that have been subjected to it, (and whose attractiveness has as a result waned), denigrate and shame those that have not been subjected to it. They want to believe that “very few men would marry a girl who has not been excised and infibulated” – an argument which fortunately is contradicted by men’s preferences.
“Sure enough, most observers conclude that the practices are most zealously defended by women. Men seem generally indifferent (consistent with Greer’s impression that the men often do not even know). Some fathers object to having their daughters subincised or infibulated, but the men’s objections are overruled by the women in the family, who insist on having the operations performed., [Researchers] also reported several findings indicating that men argued for less severe surgical practices but were thwarted by the women’s determined support for the practices”.
The authors conclude that “the evidence regarding subincision and infibulation indicates that women control and maintain the practice. This too supports the female control theory [of female sexuality] and contradicts the male control theory”.
Feminists usually try to frame FGM as an issue of male control of women, but would it not be in men's best interests to increase a woman's sexual desire for men, and not decrease it? Is it not ultimately an issue of female control over men's access to sex from women?
Of course a much more important reason to oppose the practice is the fact that it is barbaric, and that by opposing all forms of genital mutilation, we can also fight against male genital mutilation.
The rabbit hole goes pretty deep though. MRAs ought to be opposed to all forms of sexual control of women (including slut shaming), not just on moral grounds, but also because the primary purpose of it appears to exploit men's sexual desires for women.
I don't want to go down the road that feminists do where they try to frame everything as ultimately being about them. But I think this is important for MRAs to know about, if for no other reason than to correct people when they try to blame these problems on men or the illusive "patriarchy" (the cause of this problem might just be a scarcity of resources... women negotiate higher prices for sex when resources are scarce, and FGM can be directly traced to resource scarcity). Fighting against the patriarchy (if we assume it's real) will not end FGM because it is not a patriarchal institution, nor is it carried out by men. The real motivation behind the practice is something that feminists often have a problem admitting to, which potentially makes MRAs better suited to fight against it.