Why can't some people apologize?

Maybe their heart is so small that they cry before they even say anything. Or there might be another reason like not accepting their mistakes or having a short temper.

The biggest problem seems to be that certain people have ego problems, and a large amount of it is cultural. They honestly believe they are infallible or that apologizing is a sign of weakness. They may withhold an apology as a form of dominant behavior which disregards the other person. Often, it is a sign that they don't fully accept themselves - mistakes, flaws, and all.