Even for the uber-conservative parent who thinks their kiddo won't ever have pre-marital sex (and that somehow a shot will negate that kid's entire upbringing, versus...say... the more likely culprit of teenage hormones), there's always the worst case scenario of rape and I think the vaccine should be given. Shoot...say you make it to marriage without having sex, people do cheat and you might not know who else your spouse has been with during your marriage. What a horrible double whammy to have a cheating spouse and get an STD that could cause cancer.
I was raised "right."
Guess what? I didn't even know what HPV was or that a gynecologist is the doc who can test for it. My public school preached abstinence (sex will kill you dead, every time). When I was a teenager, my doc refused to prescribe various things for religious reasons. Doctors can do that in Virginia. If you're going to raise your kids this way, please protect them from their upbringing by vaccinating them.
After my first ever gyn appointment, I found out I had HPV. I had a benign strain of the virus. No clue when I got it. In college, I had an STD test every couple of years - without insurance, STD testing at the county clinic was far cheaper than a doc appointment. (And I wasn't about to ask my parents for money, especially related to sex). But it didn't include HPV testing. Or HIV, because Virginia. So even if someone was tested - far more than you can say about most college kids - you still have no clue if they have these viruses. And if you raise your kid "right," they won't know enough about this stuff to ask their partner the appropriate questions!
I got the vaccines to protect against the not-so-nice strains. No side effects.