You are implying that we mostly evolved eating meat, which is wrong. We evolved being omnivores and we ate everything we could get, mussels, large insects, fruit, tubercules... Make no mistake, humans were hunters but that was only one part of the picture.
I think you are mixing two different (although very related) terms.
We did evolve by eating meat. The archeological and even biological evidence for that is quite strong. Eating meat (more specifically fish) allowed for the necessary proteins for brain increase.
But we seem to have evolved to eat as much as possible, thereby, we evolved to be omnivorous.
The difference here is between by what diet we did evolve and to what diet we evolved to. But the by part is purely biological in nature, the to part is also a sociologic one, since it depends, amongst other factors, on the use of fire to cook.