People like to be right for a number of reasons including:
1, Absolute Ego
2. Making others look less intelligent
3. So they can say, "I told you so."
4. Just for the sake of arguing. Often with people like this, an intelligent discussion can turn into a heated argument, which was the plan of one or both of the participants. No one meets to argue. They do meet to discuss differences with the hope of it turning into an argument.