Finding reasons why evolution would favor big brains and intelligence in humans is easy. A more difficult line of inquiry is to determine if there are costs involved in having advanced intelligence, and what they may be.
“The results from our analysis suggest that humans aren’t as efficient as chimpanzees in carrying out programmed cell death. We believe this difference may have evolved as a way to increase brain size and associated cognitive ability in humans, but the cost could be an increased propensity for cancer,” said McDonald.
This particular hypothesis indicates that increased cancer rates is one significant cost.