For some people, apologizing can be very difficult. Some of them never apologize. This is unfortunate, because whether people apologize or not when they make a mistake can affect their health. I must begin my explanation with a disclaimer.
Different cultures have different approaches to apologizing.
I am writing from the bias of an Anglo-American. Your culture may be different, so please keep this in mind. When we apologize to another person, it can elicit a set of unwanted, negative emotions within ourselves. The act of apologizing indicates that we were wrong, and therefore that we are not perfect. We made a mistake.