Heard this on NPR yesterday (yes, I listen to NPR a lot).
According to the theory, mammals can have either a large gut or a large brain, but not both. Vegetarian mammals expend all their energy on digesting large quantities of vegetables & fruit. They need a big belly to be able to ingest a lot. Energy is mostly used digesting it all. But meat is easier to digest and packs a lot more calories. So energy can be used to grow a brain instead.
Next time your vegetarian friend tells you to stop eating meat, tell them you're smarter for eating it :)