I still find the behavior odd. If someone says "I feel awkward around people because I'm short" no one responds with "that's not a problem with being short, that's just social anxiety". But when someone says "I feel awkward around people because I'm smart" suddenly everyone has an issue.
There are many varieties of intelligence in many domains. If you find yourself in the company of someone you feel is less intelligent than you, try finding what they know about or care about. What have they experienced that you haven't? Or perhaps try finding a shared area of ignorance. Who knows, you might find they consider you dumb or naive in some way.
It is indeed very hard for some people to feel comfortable in social situations that are outside their prior experience or interests. But I'm inclined to agree with grandparent comment that this has little to do with 'intelligence'.