If we try to explain ourselves through observation we might plainly argue that of course, all humans are omnivores. We can look around and see that people eat many varieties of things and do not immediately suffer unhealthy consequences for diets heavy in animal flesh or in plants. But this type of analysis can be less than scientific because our actual diets can be affected by cultural, ideological, and behavioral norms. It would be more helpful to analyze the abilities of human bodies to handle these types of diets and consider the healthiness of humans who maintain these diets.
The human gastrointestinal tract shows many of the characteristics common to herbivorous animals. Humans have muscular lips with many of the facial muscles providing a range of motion while chewing. (Not found in the carnivorous animals that must have jaw muscles made for slashing or cutting through bodies.)
Human teeth with the exception of the "canines" are similar to those of herbivores.* The canines of humans are flat and blunt in a way that makes them act as augments to our incisors, rather than the conical knifelike teeth of the carnivores.
Our incisors are useful for peeling, snipping, and biting relatively soft foods like fruits and vegetables. Premolars and molars provide the rectangular shape necessary for the grinding required to process more dense vegetables and other coarse foods.
Human saliva is specially devoted to digest carbohydrates with the enzyme salivary amylase beginning the breakdown of starches as soon as food enters the mouth. Our esophaguses are designed for small, soft balls of heavily chewed food; often eating quickly or swallowing even small bits of un-chewed food will result in discomfort and often induce a gag reflex or choking in humans.
The human stomach is a single chamber and only moderately acidic. The human small intestine is long, measuring from 10 to 11 times our body length. (Compared to about 5 times body length for many carnivores.) Our colons are pouched like other herbivores, allowing for greater reabsorption of water. High fiber diets allow for extra energy absorption in the colon from volatile short-chain fatty acids.
Overall its hard to imagine an anatomical argument for humans bodies having a commitment to a fleshy diet.
Human anatomy does not show the mixed structural features one expects and finds in anatomical omnivores such as bears and raccoons. If we compare the bodies of carnivores, omnivores, and herbivores we find that humankind's GI tract is designed for a purely plant-food diet.
*The canine question brings up an interesting possibility not analyzed in this article. We have here only discussed 'herbivores' 'omnivores' and 'carnivores', but this leaves out another diet that is mostly composed of fruits. Animals like bats who eat fruit-heavy diets are often referred to as 'frugivores.' It is possible that it would be most prudent to say that human bodies are fit to eat a diet of a variety of plants, and that they can occasionally survive for short periods with cooked flesh.
You can find more on this topic here: Article by Dr. Milton Mills