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AthrillatheHunt This is just an hypothesis that's been recently critized and as for the direct reason for brain growth this has been considered to be the by product of cooking and starch, fat bioavailability.
Cooking increases calorie consumption.
https://attheu.utah.edu/facultystaff/new-study-questions-importance-of-meat-eating-in-shaping-our-evolution/
The researchers found that, when accounting for variation in sampling effort over time, there is no sustained increase in the relative amount of evidence for carnivory after the appearance of H. erectus. They note that while the raw abundance of modified bones and the number of zooarchaeological sites and levels all demonstrably increased after the appearance of H. erectus, the increases were mirrored by a corresponding rise in sampling intensity, suggesting that intensive sampling—rather than changes in human behavior—could be the cause.
We find that the apparent increase in archaeological evidence for carnivory after 2 million just reflects a better sampling of the fossil record. There’s no meaningful increase in evidence for carnivory after Homo erectus shows up on the scene,” said J. Tyler Faith, curator of archaeology at the Natural History Museum of Utah and associate professor of anthropology at the University of Utah. “Meat made us human? Not so much."