Your utter lack of understaning that every vaccine and every medicine on the market, from penicillin on down, carries risk is also noted.
You're right that every vaccine has risk. But my daughter cannot get HPV by sharing a drinking fountain or breathing the same air as another kid who has the virus. She could get measles (actually she *did* get measles... fully vaccinated, thank you) or mumps or the flu through every day contact. Much of HPV transmission can be prevented by behavior modification. As for the "the husband may have a past" argument; she can get the vaccine later if need be.
Playing the odds. What we really need to know is: How many girls have side effects from the shot? (Is it 1:1000?) What are the odds that a woman will die from cervical cancer? (Is it higher or lower?) What are the *long term* side effects of the shot? (birth defects? infertility? autoimmune disease? cancer? How can we possibly have a frickin' clue about *that* for at least 10 years?)
Until these questions are answered, I will not be giving my daughter this shot.