Why would the HPV vaccine only be pushed for women, when its known to do this to men?

For both. It is indicated for specific age groups in both males and females. It protects against cervical cancer caused by certain strains of hpv in females and genital warts caused by the hpv strains in males.
Powers that be. The decades it took to develop and bring the hpv vaccines to fda approval and distribution make it one of the costliest vaccines i give.The initial approval target that garnered the most research and support was use for females prior to hpv exposure. After approval, acceptance by the insurance companies that decide what they will cover took time. Docs would have everyone get it, payors not so much.
Both sexes. Current recommendations include both sexes due to risk of cancers in both.Otherwise dr ferguson's answer sums it up well.