Pretty much every species is subject to sexual selection: heritable characteristics that lead to more mates or better mates can be favored by natural selection. Typically, sexual selection favors different strategies in males and females. Generally, males can gain fitness with increased mating opportunities, while females gain more from high-quality mates or mates that confer resources. Since the variance in reproduction is usually greater in males than females, sexual selection is usually stronger in males, although it exists and is significant in both sexes.
Usually, though, males and females of a given species have very similar ways of making a living. A male deer and a female deer both eat grass or arugula or whatever. Sexual selection may drive them to evolve in different directions, but finding something to eat mostly drives them in the same direction.
Humans are an exception. In the long past, men hunted and women gathered. The mix varied: in Arctic regions, men produce almost all the food (while women made and repaired gear, as well as raising children). In groups like the Bushmen, women produced most of the calories, but done rightly you would count more than calories: if most of the local plants had low protein or low-quality protein (wrong amino acid mix), meat from hunting could be important out of proportion to its caloric value.
This has been going for a long time, so there must have been selection for traits that aided provisioning ability in each sex. Those job-related selective pressures probably changed with time. For example, male strength may have become less valuable when the Bushmen developed poison arrows.
I was looking for an intelligent discussion of this question – but I ran into this and couldn’t force myself to read further: ” It should not simply be assumed that the exclusion of women from hunting rests upon “natural” physiological differences. ”
God give me strength.