As a longtime vegetarian and vegan, I've come across the false claim that our higher intelligence evolved because we ate a disproportionately hgh amount of protein, in the form of the corpses of other living beings. If that were the case, then every lion would be about as smart as Einstein.
It's also said that we need large amounts of protein. Again, rather than get into petty bickering and he-said-she-said, I'll point out that the Mountain Gorilla is nearly entirely vegan (the exceptions being insects, most of which are incidental, on the leaves they eat.) I'll also point out the some of the largest, most powerful beings on the planet are likewise plant eaters. The elephant, for one example, eats no flesh, is highly intelligent, large and powerful.
Please, other contributors, feel free to debunk other claims below!