They take it personally
Many people take arguments personally, and as a result, they do their best to win them. In such a case, the person sees losing the argument as one kind of bad loss.
They want to be right
Some people don’t care about what’s right and what’s wrong as long as they are proven right. The desire to be right motivates people to argue.
They can’t give up the wrong beliefs
Some people develop certain beliefs in order to maintain their psychological stability. Those people don’t argue to find what’s right, but to protect their already existing beliefs.
They don’t want to seem agreeable
Some people don’t like to be seen as agreeable, especially males, and as a result, they might object or argue just to prove that they have a different opinion.
They question everything
Some people question everything they learn, and as a result, they appear to be arguing about everything. Skeptic people, for example, are more likely to argue than others.
To protect a different belief
Sometimes a person might argue about one thing in order to protect a totally different belief that they have even if that belief isn’t mentioned directly in the argument.
They believe they are always right
Some people believe they are always right. Those people hate it when others argue with them, and as a result, they might argue about big and small matters.
They are narcissists
Narcissists are very likely to argue with people for they hate to be proven wrong. Narcissists believe that they are superior to others and so they consider most people not as informed as they are. (See What Makes a Person a Narcissist?)
The matter is very important
Some people like to argue when they believe that the matter being discussed is very important. In such a case, those people might argue a lot when it comes to that specific topic.
They get a self-esteem boost
Some people argue a lot because they get a self-esteem boost when they prove themselves right or when others can’t continue debating with them.
They want to change someone’s belief
If a person is concerned about another, they might try to change their beliefs. A parent concerned about their children, for example, could try to convince them over and over that smoking is bad. (See Why are some people very pessimistic?)