Michael Pollan had a great quote with regard to this very issue, that was roughly:
"There's abundant evidence that humans have lived healthily on a large variety of diets which makes it all the more surprising that western civilization has hit on the singular diet that makes us ill."
There's evidence in the anthropological literature any way you want to spin it for a predominantly plant based, predominantly animal based, higher in fat, lower in fat, higher in saturated fat, lower in saturated fat, this macronutrient ratio vs that one, etc. etc., etc., because humans have lived very healthily on all of the above.
The one diet that seems to consistently fail is where the food chain is based nearly exclusively on grains (directly and through consumed animals), processed oils (vegetable oils and transfats), and sugars.