You misunderstand what "natural" means. Nature doesn't care at all about those things. But as a social species, we evolved some "rules" which ensure our survival. In that sense, some of our morality has roots in nature and evolution.

So I don't agree at all that by not using violence all the time we're going against our nature.

But in the case of food, I believe we are, because evidently we require certain substances to survive, and one of the best ways to get those is to eat meat. In most regions where humans live today, without meat or foods imported from faraway regions, we couldn't survive.