The vaccine needs to be administered while they are still virgins, so the public health benefit is delayed. Also, FYI, those HPVs also cause cancers in men. There is no reason not to have sons vaccinated, as well.
Not just that males have some risk (probably smaller than females), but if the point is to eradicate the virus, then it is essential to vaccinate the males half of the population, as they carry the virus. It would be essential to vaccinate the males even if there was ZERO risk to males from HPV infection.
Not that I'm advocating the vaccine, just pointing out that if one adopts the objective of eradicating HPV, then the vaccine must be mandatory for "everybody."
Same when a vaccine is developed for AIDS.