Males hunt for demonstration of dominance and sexual prowess.
From an evolutionary standpoint, primates have always been plant-based over their 85 million year existence as a species. Opportunistic scavenging of animal organ meat and marrow was an occasional more recent practice. Only until cooking became a means to process meat about 200,000 years ago did animal flesh become a chewable, digestible option.
Not until about 40,000 years ago was there any true hunting with projectile weapons. Harvard anthropologist Richard Wrangham and his colleagues have claimed that cooked tubers alone played a more important role than cooked meat in our ancestral dietary transitions.
Wrangham argues that meat was not an important source of food but rather hunting itself was considered an important behavior, less efficient than foraging for plants and thus possible only if supported by gains in efficiency such as provided by cooking plants.
Their hypothesis is that sexual alliances emerged from the adoption of cooking plant foods foraged and then processed by females, and that no other dietary plant had the same potency for promoting sexual bonds as cooked underground storage organs, with their high energy yield, predictable collecting locations, and increased value as a result of cooking. Apparently the men wandering off hunting/ scavenging met with quite variable results.
As a contemporary comparison, the chimpanzee cooperative “monkey hunt” and subsequent sharing of food is a most dramatic example of meat-eating within the nonhuman primates. It is opportunistic rather than planned, and it has been suggested that chimpanzee hunting yields more social than nutritional benefits . For example, female chimpanzees are more likely to have sex with males who have shared meat with them than with those that have not.
Read more in "The New Ancestral Diet".
Wrangham, R., Jones, J., Laden, G., Pilbeam, D., & Conklin‐Brittain, N. (1999). The Raw and the Stolen: Cooking and the Ecology of Human Origins. Current Anthropology, 40(5), 567-594
Stanford, C. (1998). Chimpanzee and red colobus: The ecology of predator and prey. Cambridge, Mass.: Harvard University Press.
Gomes, C., & Boesch, C. (2009). Wild Chimpanzees Exchange Meat for Sex on a Long-Term Basis. PLoS ONE, 4(5116).