This is a crucial idea for kids struggling with social skills. Often, kids on the autism spectrum and those with Asperger's are very concrete thinkers. For them, an apology can be invested with so much heavy meaning, things like, "I don't have to apologize because it was an accident," or, "I already feel bad, I shouldn't have to keep talking about it," or, " He was mean to me yesterday. Now we're even." Other kids may not have a heavy meaning. Instead they get so overwhelmed, and feel so bad, and get so stressed that everyone is looking at them, and now the teacher is demanding an apology, and... You get my point, the apologizing can quickly get overwhelming.
Try to teach your kids the art of apologizing. It goes a long way toward smoothing relationships.