The most likely hypothesis about how humans have become the most efficient hunters of the planet does not pass through catching insects and very small animals, but through eating the remains of the big prey killed by carnivores.

There are various bits of evidence for this, like the higher stomach acidity of humans, which resembles that of carrion eaters, like hyenas.

It is plausible that the ability to throw sticks and stones was used initially for scaring other predators and make them abandon their prey, and only later, after hundreds of thousands of years of evolution, it became accurate enough to be usable for hunting living animals.

The ability to use stones to break the bones and eat the parts inaccessible for the carnivores who had killed the prey, i.e. marrow and brain, which are rich in hard to get nutrients, e.g. omega-3 fatty acids, is also presumed to have played an important role in the development of a bigger and bigger brain.

It is likely that the gangs of humans acted in a very similar way with the packs of hyenas, which acquire much of their food by scaring away from their prey the other predators, e.g. cheetahs, wild dogs, leopards and even lions. Moreover, similarly to humans, the most important ability of hyenas is not speed, but endurance when pursuing a possible prey that is tired or weakened, e.g. by wounds. While hyenas rely on their big teeth to chase the other predators, humans have relied on their ability to throw things at a distance, for the same purpose. While humans are quite bad at running, jumping, climbing or swimming, in comparison with most mammals, their throwing ability is unmatched by any other animal.