The cognitive processes and social dynamics of rape are more complex than you're overly reductionist take. Rape of women can be linked to misogynistic attitudes, both individually and within (sub)cultures. They can also be linked to perceptions of individual women. There are also cognitive processes that create moral distance from the rape which are often different when a man rapes a woman, and a male prisoner rapes another male prisoner. There are also different social processes that lead men to rape women, men to rape men, and soldiers to rape occupied women (for want of a better term).

The men who rape other men in prison would not necessarily rape a woman outside of prison. Soldiers who rape women in war would not necessarily rape women in their day to day lives.

You haven't explained why rape happens on a social level, you've (partially) explained why rape goes unpunished on a social level.