Well, actually humans are omnivores. We have not been eating grains for very long given our gastronomic history. Early men and women ate meat (raw usually) and green plants, fruits and nuts. This model is now being touted as the "caveman diet" for maintaining good health.
It differs from the high-protein Atkins model because it allows fruit (a natural and most nutritious food for humans!)
Our teeth are made for tearing flesh, and also for grinding plants. Quite a machine is the human body. Our intestines are made such that they require a large amount of fibrous material to move waste matter efficiently. In primitive cultures a bowel movement after every meal in the norm. In the USA and other industrialized nations, one is the norm (and for some not even that). Little wonder we are addicted to drugs that do this work for us, and that the types of cancers and disorders prevalent in our society are almost entirely due to poor digestion and elimination. These diseases were unknown in early mankind.

Also there was far less FAT on the animals our ancestors ate, as compared to the ones we eat now that are raised for slaughter (don't get me started on the hormones and antibiotics pumped into our chickens cows and others--DO try to eat naturally-raised animals, it's better for us and more human for them).
AND last but not least, umans were far more ACTIVE back then; and we did not eat three squares a day. The rituals and ceremonies surroudning the hunt were significant: a successful hunt meant food for a short period of time. It took days and sometimes weeks of tracking and hunting to get that caribu that would feed the family for a few weeks...so humans' bodies learned to store fat effectively. Now, since we eat way more and exercise a lot less, we store it TOO efficiently...

As for grains, they combine protein and carbohydrate in one food. Some nutritionists say this is not good because the human body cannot digest both at the same time efficiently because of the digestive acids required for both. This is one of the principles behind food combining diets and Atkins to some extent. Some people do fine with grains; some do not. I know if I eat a sandwich on whole-grain bread every day for a week I get kinda bloated, and eating too much pasta is bad for anyone unless it's the whole grain variety.

Balance in all things...

Eat more fruits and veggies, organic if possible. Go easy on the fatty meats, and eat more lean protein, and less of it that you think you want. Drink more water, and get more exercise. Live longer if you're happy and lucky!