The most dangerous meats are ones originating from wild animals. Eg there are all sorts of nasty parasite cysts in wild boar meat. Nature is brutal and there is no such thing as "clean" meat from wild animals. Human inability to deal with this and becoming severely sick without thoroughly cooking the wild meat is evidence that even if we technically are somewhere on omnivore spectrum, we're not really good omnivores—certainly not as good as bears or even boars. Honestly, eating insects, honey and eggs in addition to plants (fruit specifically) seems more like what we're evolved to do.