I think your correlation is faulty. In African countries people don't eat much, many are basically on low calorie diets. There's not much over-intake over carbs there. So if you just eat carbs and vegetables in moderation, the risk of cancer is probably very low. In the West we eat more meat, but we also over-eat like crazy, we're exposed to tons of chemicals, stress, sugar, seed oils, processed foods, so a large percentage of the population get diabetes, heart disease and cancer. I think the best diet for humans is probably something closer to a raw / low heat paleo diet with meat, organs and some carbs here and there.