Some monkeys are omnivorous, but few are as convincing omnivores as bears or pigs, as the diagram below clearly indicates, primates are predominantly foli-frugivores. The faunivores are preominantly insectivorous species, not carnivores. These are small bodied primates, often weighing as little as 60-80 grams. They have special adaptions to their particular diet, including keen sense of smell, appropriate teeth and claws or hooves for gaining access to or dealing with prey. Primates do not have these.
Some lower primates do use their hands to capture and hold prey however.
Hands are suited to a variety of purposes. These lower primates are of small body size and their metabolism is in need of concentrated nutrients. Comparative Physiology is the science of comparing animal physiology Humans may well have certain charateristics in the physiology of their digestive systems that make them appear to be suited to meat eating, but these are contraversial, and are not reflected in dental anatomy or metabolic requirements. This is despite the fact that they lack the bacterial or endogenous enzyme capacity to digest cellulose. The bear has the flattened molars typical of herbivores as well as teeth to help it tear at flesh.