We have large brains due to social interaction. In early societies culture meant things had to be remembered. Another important function leading to large brains was tools use, though chimpanzees use tools. The most intelligent people would inevitably become leaders and have the choice of mates, thus passing on their genes.
Intelligence and brain size are of course interdependent. Animals such as dolphins and elephants have social structures. They are also very intelligent. Higher intelligence appears to be naturally selected for in any species.
Apparently, when society develops intelligence must increase otherwise an individual will be "put upon" by the smarter ones. There is some evidence that really clever individuals tend to be disruptive to a society. The naive are certainly at a disadvantage.
A thorn in the side of the above theory is that some highly structured societies are composed of small creatures with tiny brains. Ants, bees and wasps are in this category.
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