I assume that by this question in this section you are suggesting that human physiology is very similar to that of chimpanzees so as such, we should follow a diet similar to a chimpanzee?
If this is not the case, then this question properly belongs in Y!A's zoology section . If this is the case then there are many fatal flaws in your argument.
If you do not have a long attention span, move on, because this is going to be a long answer as I have seen variations of this question many times and I want to use Jane Goodall's critique of Katharine Milton's work to firmly put this myth to bed.
Trying to make comparisons between humans and chimpanzees. This stems from erroneous over identification of the similarities in physiology and chromosomes between humans and chimpanzees, which totally ignores the most basic scientific evidence, biology, biological processes and the way man has changed his diet through cultural practice. Then it leads to erroneously trying to connect a 'natural human diet' with that of a chimpanzee and making incorrect assessments as to what a chimpanzee naturally eats.
Chimpanzee diets are well researched (see Goodall and Conklin references below). The proportion of flesh/insects in their diet is very small. Studies by Goodall and Conklin show by time that about (4 - 5.4%) is flesh/insects. This figure (Goodall 4% insects, meat 1.4% ) is largely made up by insects which is largely a social activity, not for nutritional gain as the energy expended to catch these termites by fishing far outstrips the energy gained. Termite fishing (the main source of insects that made up the 4% of the diet) is a highly seasonal, opportunistic activity (carried out in the month of November), it is NOT part of their daily diet. It is a cultural activity, not a nutritional need for calories. SOME groups of chimpanzees termite fish, others do not, if it was a nutritional need it would be seen across all chimpanzee cultural groups AND it would be eaten on a daily/weekly basis. So as that can now be dismissed as being nutritionally insignificant we return to the Meat.
Please note MEAT makes up only 1.4% of their diet which in any statistical study or analysis would be considered as quantitatively unimportant. In longitudinal studies it has been found that 90% of all kills were by males and as the females rarely hunt they receive a share in return by begging only after she allows him to mate with her. The importance of meat is that it is used as a political tool, which can also be seen by the way it is distributed within the group. On rare occasions chimps do eat and kill a baby chimp. So if you follow this argument to its conclusion, humans should kill and eat their babies, meat should only make up 1.4% of the human diet but females should only receive meat by begging for it and allowing the giver to mate with her!
But for the sake of this Answer and to make it easier to point out fatal flaw No 2 lets PRETEND that the 1.4% of Meat in the diet is significant and totally ignore reality that this 1.4% is nutritionally insignificant and their diet is made up from 69% fruit, 25% leaves and 6% seeds. To do this we have to totally ignore the most elemental human and chimpanzee biology and biological processes. We also have to ignore the way that chimps 'eat' meat; they put the meat between leaves and chew extracting the juices, these sandwiches are then, most commonly, discarded and not actually swallowed at all. Proteins and fats are much easier to obtain from nuts and seeds. When chimps do swallow these sandwiches there is a high presence of undigested (so unassimilated) meat in their feces.
We then have to ignore that we, humans, are NOT chimps. We also do not have: The biology to eat meat or the complex digestive chemistry, absorptive, transportive, and assimilative biochemistry, the tooth structure, claws, the ability to outrun other animals, or the instinct. When was the last time you actually ran outside and with your hands and teeth actually caught an animal, tore it to pieces with your hands and teeth and then ate it RAW? There is overwhelming epidemiological evidence that meat and dairy consumption are key causal factors in many of man's degenerative diseases.
To suggest that humans are like chimpanzees and should therefore eat a diet high in meat is just totally erroneous it ignores overwhelming evidence to the contrary and almost all accepted scientific data to date.
A critique of: A hypothesis to Explain the Role of Meat Eating in Human Evolution by Katharine Milton by Jane Goodall.
Scientifically credible information on Vegan and Vegetarian diets
Goodall, Jane, The Chimpanzees of Gombe, Belknap Press of Harvard University Press, Cambridge, MA (1986), p. 233
Lehninger, Principles of Biochemistry, Worth Pub., (1982), p. 158.
Graph showing primate diets