Mammalian reproductive strategies.
Placental mammals have internal fertilization, and the females carry the young internally. Males have a much lower physiologic contribution to the offspring, whereas females have a very resource contribution. And males typically are able to potentially fertilize many females in a mating season, while females can typically have only one litter, it doesn’t matter how many males they mate with.
This means that males typically contribute almost no parental care to the offspring, whereas females typically contribute a great deal. Males are able to “walk away” after mating, whereas females cannot. Contrast this with birds, where both males and females are able to walk away from the eggs. In birds, males often contribute a great deal to parental care.
So we have males competing to reproduce. There are many ways they can do this, but often this means physical competition. Male sheep butt heads, so male sheep have bigger horns, stronger necks, and larger body size. Female sheep are a more optimum size, but a male sheep the size of a typical female sheep would have lower reproductive success than a larger male. So large size is a secondary sexual characteristic.
When we look at primates, we find the same thing. Male gorillas are often more than twice the size of female gorillas, same with male orangutans. Male chimps are larger than female chimps. And male humans are about 10-20% larger than female humans. But, lets look at gibbons. Males and females form lifelong pairs. Males hardly ever compete for females. Gibbons don’t have much sexual dimorphism. And male gibbons contribute a lot of parental care. Male humans are somewhere in the middle between the extremely dimorphic gorillas and orangs, where there is a lot of male-male competition for mates, and the extremely non-dimorphic gibbons, where there is almost no direct male-male competion.
And when we look at human social groups, we find that humans typically form long term pair bonds like gibbons do, but that high-status males often have multiple females.
So…male humans are larger and stronger than female humans because males have had to physically struggle for the right to mate with female humans during human evolutionary history. We have less direct competion than some of our relatives, but more than others. Also, we might speculate that competition has had some mental effects too. When women take testosterone they often find they get angry more easily, they feel more violent and competitive. It wouldn’t suprise me that men are more interested in competitive activities even when those activities aren’t physical.