The major pro is that the vaccine can help to stop the spread of HPV. That is a big deal. The only real con that I have heard (according to some) is that some people feel that the vaccine will encourage promiscuity. Some people think that their kids will go out and sleep around if they don't have to fear HPV.
Infection with Human Papilloma Virus (HPV) is the most common sexually transmitted disease. It is estimated that 20 million individuals are infected with HPV and 6.2 million new infections occur each year. Although most infections are benign, persistent infections are associated with cervical cancer in women and genital warts in both women and men.
Researchers say that the prophylactic administration of quadrivalent vaccine is 96% effective in preventing infection with HPV strains 6, 11, 16 and 18. Also the bivalent vaccine has an efficacy of 96% in women seronegative at the time of vaccination. However, the effects of this vaccine will be assessed over several decades, this fact raising questions about the statistics on its effectiveness.