It is more likely that our brains got larger because we learned how to cook, both plant food and meat. However, considering that early humans ate very little meat, it may not be accurate to say that consumption of animal fat and protein was the main reason.Considering the human species was able to evolve larger brains due to the consumption of a lot of animal fat and protein, that does make some degree of sense. Over the long term, if the human species fails to take advantage of those high-energy food sources, those big brains it is so infatuated with will indeed be threatened, particularly once unsustainable industrial agriculture collapses.
http://cogweb.ucla.edu/Abstracts/Pennisi_99.html