It shouldn't be mandated. People should have the right to be as stupid as they want and if they don't want to get their kid this vaccine, then that is pretty stupid.
People get too hung up on the word “sex”. This is not a vaccine given via the vagina. It is a shot in the arm and no kid (unless they are told) will know what it is, and even if they did, they wouldn't equate it to a ticket to free sex. Any kid that would be having sex because of this would already be having it any way.
The only possible downside to this is that it is new and there might be some long term issue with it. I think it was rushed out of trials because it had the potential to save so many people. That is a little worrisome, but to rage against this, because it stops a sexually transfered virus from giving people cancer is lunacy.
Perhaps if there was a vaccine that stopped people from having children for the next 10 years and it was given to girls at the age of 11, then YES that might cause a rise in sexual activity (if that vaccine existed though would more sexual activity be a bad thing?). I seriously doubt that there are that many kids NOT having sex because they think they might catch hpv. I mean how many kids even know HPV exists? In all the stuff I was told about sexually transmitted diseases in health class, HPV was never even mentioned.
Why do most people not want kids to have sex? That is an easy answer, the main reason is that they don't want the kids having kids. Disease, harm and religion are all secondary to that (and I would say that religion is probably based on not wanting “kids to have kids”, but the bible has to say God said it, not list a valid reason.) Well this vaccine doesn't stop kids from getting pregnant (and there is very little chance someone would think that it did), so why does everyone think that it will make them start having sex more?
People should start thinking with their brains instead of just having jerk reactions to words and phrases.