People who don't think clearly often need for you to boast if they are to treat you respectfully. They only go on credentials and how much you boast, rather than evaluating evidence, so if you don't boast, they think you must not be any good. These same people, though, hate boasting more than smart people do. That doesn't alter the fact that if you don't boast, they'll think you're no good. If you do boast, they'll think you're smart, but just not a nice guy. On the other hand, smart people don't mind boasting so much, I find, because they treat it as harmless verbiage that wouldn't have any practical importance.
Also, what is boasting differs. If you tell some people you were just on the phone with a Harvard professor, they'll think you're boasting and name dropping. If you're on the phone with a Harvard professor every day, though, and half the people in your family went to Harvard, and all the really smart ones went to MIT, you don't think it's boasting.