Looking at the animal kingdom primarily males fight among themselves to gain the mating rights of the females. Once a dominant male gains the control, the male has reproductive rights to a harem of females. Even though females have the capacity to fight back to save the current dominant male from the new opposing male, they simply accept the change of dominant male, which proves that females actually want males to fight each other for the betterment of offspring.
Men do fight; both literally and figuratively. Physical fights like fist fights or warfare are a lot more damaging than proxy competition like a game of chess. Men achieved various means of proxy competition by practicing arts, music, sports, architecture, professions, etc. which gives individual men an opportunity to stand out from others. This allows men to have less violent conflict and yet still compete with other men. Even though these activities mostly arise when men are still single, without women in mind, these skills allow them to later benefit from being chosen by women. Since women mostly look for resources and status, such proxy competition is a win-win for both sexes as it brings both resources and status to men.
Of course there are some activities among men, not practiced as widely as other activities, which tend to be seen by women as weak or gay, and does not bring social status to men. Some of them are roller skating, playing carroms, etc. and such activities remain niche in society.
In this way, men have innovatively created a way to avoid physical fighting in the drive to gain reproductive rights with women by engaging in proxy warfare.