It has to do with belittlement: an audience's feeling of being dissed, and its desire to see the culprit shrink. The problem is, big stars don't want to become little planets.
So how does a bigshot--or you, for that matter--apologize without shrinking? Follow these steps:
- Own up to the mistake. Tell the truth, the whole truth, and nothing but the truth.
- Focus on your emotions, not how you hurt someone else. Say how bad you feel about screwing up.
- Show how your mistake was an exception to the rule. You're a great, thoughtful person who temporarily lapsed.
- Promise improvement and show what you're going to do to fix any remaining problems.
Here's a video I did with details.