Being able to make a sincere apology - one that says, "Yes, I get it; I screwed up. Your feelings make sense, and I'm taking this seriously" - is at the heart of being successful in leadership, parenting, and friendship, as well as our own integrity and self-worth. And the failure to apologize? Even a good relationship will suffer quietly - because we really feel it when someone won't take responsibility for what they said, or didn't say.