What are the evolutionary explanations for why women are weaker than men (on average), and is this difference adaptive? I suppose that something puts pressure on men to be stronger than women, but I don't see what it can be. Why the discrepancy between the sexes?
All of the theories surrounding this fact are speculative; it would be difficult to prove "why" men are, on average, stronger than women.
One contributing theory is Female-Choice - basically that women had (or has) the ability to be more selective when it comes to choosing a mate. Over time men will reflect the preferences of women (taller than them, stronger than them, facial hair qualities, etc.). This is superficially supported by casual studies like the linked one where the "attractiveness" curve for men is down-shifted, meaning women think the average man looks below average in attractiveness and implying those who are viewed as average ( actually the top 20% of men or so) would have better reproductive success. Men, in the same casual study, had a nearly perfect bell-curve associated the attractiveness of women, implying that men are excellent at deducing whether a women is below average in attractiveness, average, or above average in attractiveness.
Another contributing theory is Male-Male Competition. Basically men, at some point (and still might) compete with other men to win over women. The bigger, stronger man would presumably win in a fight and eliminate his competition - directly preventing the production of offspring by the weaker male. The male-male competition also holds true in a more speculative theory in that the winners of wars literally raped their way to reproductive success.
It is worth noting that men, on average, are only about 30-40% stronger than women due to the larger muscle fibers in men (as cross-sectional area determines muscle strength, not volume). With training the difference (kg for kg) is reduced to 15-20%.
Ultimately why women are weaker than men (or men are stronger than women - whichever way you prefer to put it) doesn't have a solid answer beyond "because the stronger, taller men have reproduced".
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