What everybody "knows" about female circumcision:
"There are no health benefits to female circumcision. That practice exists to limit or eliminate sexual desire in women. They're two very different things. It's performed on girls 8-12 years in the bushes with rusty blades and pieces of glass with the girls crying and no pain management."
What people don't know about female circumcision:
It's not so different. There are 4 identified types of female circumcision. One of them is the removal of the clitoral hood, which is the exact same structure as the male foreskin. Other form of "circumcision" scratches the surface of the clitoris.
Even the AAP, in 2010, acknowledged that "some forms of FGC are less extensive than the newborn male circumcision commonly performed in the West".
The thing is, everybody has seen the photos of the teenage girls restrained and crying in the bushes in Africa with a puddle of blood. But in other places, such as Malaysia and Egypt, female circumcision is practiced in hospitals and doctors office, with sterile equipment, on babies (usually around 3 months), and it looks SO MUCH just like male circumcision in the West.
As for female circumcision being meant to "limit or eliminate sexual desire", I saw one Malaysian woman (who was circumcised and took her daughter to circumcise) affirm that she did not believe that. Very much like a lot of circumcised men who affirm "I'm just fine".
And yet you may not know that male circumcision was always meant to reduce male pleasure (and also make sex less pleasurable for the female partner). Per "The Guide For The Perplexed" by Moses Maimonides (XII Century Jewish philosopher): “As regards circumcision, I think that one of its objects is to limit sexual intercourse, and to weaken the organ of generation as far as possible, and thus cause man to be moderate."
First century C.E. Jewish philosopher Philo, said that "circumcision represents the excision of the pleasure of sex, which bewitches the mind... thus making circumcision the figure of the excision of excessive and superfluous pleasure" (Philo, Special Laws 2-11.)
And if we move to US and UK and the beginning of the "medical practice" of circumcision, late XIX and early XX century, you will find gems like this: "In cases of masturbation we must, I believe, break the habit by inducing such a condition of the parts as will cause too much local suffering to allow of the practice to be continued. For this purpose, if the prepuce is long, we may circumcise the male patient with present and probably with future advantages; the operation, too, should not be performed under chloroform, so that the pain experienced may be associated with the habit we wish to eradicate." On An Injurious Habit Occasionally Met with in Infancy and Early Childhood, Athol A. W. Johnson. The Lancet, vol. 1 (7 April 1860): pp. 344-345.
And in 1935 (75 years later): "I suggest that all male children should be circumcised. This is "against nature", but that is exactly the reason why it should be done. Nature intends that the adolescent male shall copulate as often and as promiscuously as possible, and to that end covers the sensitive glans so that it shall be ever ready to receive stimuli. Civilization, on the contrary, requires chastity, and the glans of the circumcised rapidly assumes a leathery texture less sensitive than skin. Thus the adolescent has his attention drawn to his penis much less often. I am convinced that masturbation is much less common in the circumcised. With these considerations in view it does not seem apt to argue that 'God knows best how to make little boys.'" R.W. Cockshut. Circumcision. British Medical Journal, Vol.2 (1935): p.764.
It's only since the 60's that the doctors have been insisting that male circumcision does not affect sexual pleasure, but then at that time, those doctors had been circumcised as babies and didn't know any different.
As for supposed health benefits (and I'm not advocating female circumcision), the main "new" argument for male circumcision is that it "reduces the chance of contracting HIV by up to 60%" (which is the result of very flawed experiments. However by the same time those experiments were ran, this took place:
A study in Tanzania ("Female Circumcision and HIV Infection in Tanzania: for Better or for Worse?
Rebecca Y. Stallings and Emilian Karugendo"), which had the purpose of finding if female circumcision increased the risk of HIV, found a "surprising and perplexing significant inverse association between reported female circumcision and HIV seropositivity", which would seem as a benefit, but they concluded that "no biological mechanism seems plausible, we conclude that it is due to irreducible confounding".
If we are to consider the theory (which has not been proved) that HIV targets the Langerhans cells present in the inner part of the foreskin, well those cells are also present in the female clitoral hood, so in a way it would make sense that the removal of those cells would have the same effect on both genders, whether the effect is beneficial, detrimental or neutral. Of course there's more to the male to female transmission of HIV.
Many of the supposed health benefits of male circumcision are overinflated. For example, penile cancer is not common and only happens in old age. You would need thousands of circumcisions to prevent a single case of penile cancer - and there would be a lot of collateral damage.
HPV can be prevented with a vaccine rather than an amputation. UTIs can be treated with antibiotics, just like in females.
Similarly, those who advocate FGM argue "health benefits" such as: "protects the health of a woman. Infibulation prevents the uterus from falling out [uterine prolapse], leaving a girl intact endangers both her husband and her baby. If the baby's head touches the uncut clitoris during birth, the baby will be born hydrocephalic [excess cranial fluid]. The milk of the mother will become poisonous. If a man's penis touches a woman's clitoris he will become impotent." We consider those statements are simply false. But just like that, most of the world consider the claimed benefits of male circumcision to be just not worth.
The core of the issue
Whether male or female circumcision have or not any health benefits, and whether they are more or less severe, it remains true that both are performed on vulnerable minors without regard for their well being, generally with good intentions from their parents. Both are invasive procedures that are not essential for the well-being of the child, that are risky for the child, and that may affect the child's future sexual life.
According to Wikipedia: "FGM has immediate and late complications. Immediate complications are increased when FGM is performed in traditional ways, and without access to medical resources: the procedure is extremely painful and a bleeding complication can be fatal. Other immediate complications include acute urinary retention, urinary infection, wound infection, septicemia, tetanus, and in case of unsterilized and reused instruments, hepatitis and HIV."
Male circumcision, however, is also extremely painful, the main two risks are bleeding and infections, a complication of the plastibell method is urinary retention, septicemia is also a major life-threatening risk, and in the case of unsterilized and reused instruments (as in ritual circumcision in Africa), HIv is also a risk.
See the difference there? I don't see it either.