Why do people always have to compare themselves to someone else to see if they know more than the other?

Answer 1

because they want to show off how smart they are. Second reason might be they want to prove they are well educated.

Answer 2

Either they are totally impressed with themselves and want to make sure everyone else has equal opportunity to be impressed with them also or they are insecure and need to make themselves look better than others around them. Unfortunately that kind of behavior has just the opposite effect.