If Chomsky believes cheering for your classmates is stupid, then he must believe that we should be perfectly objective and treat everyone exactly the same. If you're a judge or President, you have an obligation to the public to act that way. But me, I'm glad I have the luxury of showing preference to my friends and family. I care about my neighbors more than people on the other side of the world. And yes, I will root for my home team and cheer when they win.
I don't believe it's irrational or wrong to play favorites this way. And even if it were, it's so fundamental to being human that we could not be any other way. Perhaps we are a jingoistic species.