Would you coerce a parent to have a child vaccinated for any communicable disease? Measles? Chicken Pox? Diphtheria? Polio?
Well we've been seeing evidence of so called 'herd immunity' breaking down because misguided parents bought the vaccine causes autism bunkum. Among the many advances made in public health over the last 150 years or so is near universal vaccination for common infectious disease.
If you don't want your kid vaccinated then go the 'opt out' route.
Or home school. Or move.
Yes, because the vaccines are proven to not be life threatening - and anyone can get the above mentioned diseases by casual contact, such as sitting in a desk next to an infected child. The emphasis here is, this is not a lifestyle choice, but by mere proximity to an infected child, others will be endangered.
HPV requires sexual activity. I cannot infect your daughters (if I were infected myself) by casual contact. It's physically impossible - that's the difference.
Now, would I suggest my daughters get the injection? Absolutely. But, do I want Big Goverment/Big Brother dictating that they WILL by default be injected, unless I sign an afadavit? Absolutely not. Let's go one step further. I have now signed an afadavit that opts my daughters from getting the HPV virus; will I now be charged with reckless child endangerment?