The size of the brain is much less important than the brain to body mass ratio. Several animals have larger brains than humans (elephants being one), but they all have large bodies as well:
No, not really. What sets a human and elephant apart is not how smart an individual human is compared to an individual elephant, but the ability to communicate. Human language is Turing complete, art is basically communication for the sake of communication, and our perhaps most popular form of entertainment is making up stories and sharing them. That's the draw of this very website, and even now I'm using it to serialize a particular neural network - an idea - which you then can deserialize at your leisure.
Almost all human beings who have ever lived are part of a single millenia-old, planet-spanning superorganism we call "culture". It doesn't matter how much gray matter an elephant might be lugging around, it can't even begin to compare to the ~ 100 billion kg total for human species, even with all the issues with coordinating that mass.
And we're getting better at that coordination, too.