Why do some people desperately need an apology?

Some people feel wronged and will not move on with a relationship until they feel the other person is sorry for what they did. Some people will not apologize. I realize that the people who never apologize are suffering from low self-esteem, but why is an apology SO important to some people? Let's assume that the offense is a real one, and that an apology is the right thing to do, in the circumstance, especially if you say you love someone. Is it because of childhood issues? If so, what kind of treatment as a child would make an apology so important? What do you do if you are one of these people and you love someone who never apologizes? How do you cope if you never get the apology you need?