Human males are bigger than females because.... by Ryan Gregory. The answer seems to be we do not really know. "In humans, males tend on average to be larger, to mature later, and to age and die sooner than females. It’s easy to assume, as many people do, that this difference between males and females — what biologists call sexual dimorphism — is the result of sexual selection. That is, males are larger because they fight each other over access to females and/or females prefer to mate with larger males. That is a valid hypothesis, of course — but too often it is simply accepted as fact and then used as a starting point for discussing other male and female traits. As a recent example, consider the debate that is happening on the blogosphere about sexual dimorphism in humans, and whether objections to the standard explanation of fightin’ males is merely political." For the terms used check http://evolution.berkeley.edu/evolibrary/article/evo_02 and another view of the Clyne-Dunsworth debate see also How do we know what we know? Sexual selection, in humans and in lizards by Ambika Klamath. P.Z.Myers also discusses Clyne-Dunsworth debate and also the article of Ryan Gregory above in Natural selection is not the only mechanism of evolution.