Cockatiels also have an uncanny intelligence - they recognize different people, behave and play differently with each one of them, I always wonder how idle my surplus of 1298g of brain is...
The claim is that while humans may be able to master a large number of different skills, few of them are limited to humans in and of themselves (and not available to some other animals as well).
Besides, obsolete and unused brain tissue is very expensive calorically to maintain, and would be a hinderance to survival over long periods of time.