By your logic, obligate carnivores would have the larger brains. Humans are obligate omnivores. Studies show no significant differences in cognitive function, cardiovascular risk, or bone health when vegan diets meet recommended dietary allowance levels. Animal protein contributed during the evolution of the human brain, but the development was driven by cooking. Cooking externalized the energy required for digesting food, which allowed for a reduction of jaws/jaw muscles, and especially gut size, freeing energy that could be used by the brain instead.

Also, the brain is fueled by glucose, not protein …