The Harvard Business Review reverses the focus of apologies, from persuading to restoring integrity. Rising out of our failures, we can consider the gap between failed performance and aspiration.
Joseph Grenny writes (excerpt):
Issue the apology—for the right reason. The best apology is a glimpse into your own accountability. It affords others an intimate and sincere view of your internal moral conversation—how you respond to their feelings and how you judge your own actions. Its goal is not to “get” something from the other person. That decision is up to them. Some people forgive slowly and some readily. You can’t control that. All you can control is the speed with which you regain your own integrity.