Why aren't animals with larger brains more intelligent than us?

There are two reasons. First, brain structure is more important than brain size, and human brains with their highly folded and complicated cortex can do things no other brains can.

Second, relative size is more important than absolute size. The ratio of brain weight to body weight is about 1:5000 for fish, 1:220 for birds and 1:180 for mammals, with the most intelligent species generally having the highest ratio. For example magpies and crows have a higher ratio than most birds, and social mammals such as chimpanzees and dolphins have a higher ratio than other mammals. The human ratio is highest at about 1:50.

Another example is the largest brain of all belonging to the sperm whale, dolphins a relative however have a higher ratio and apart from primates seem the highest up on the intelligence scale of the animal kingdom. Dolphins can recognise themselves in a mirror, a test which has been used on babies to see when a sense of self kicks in (it turns out our sense of self kicks in at between 13 and 22 months) and are capable of imitation and highly complex communication.

What they think of us humans though we just don't know.