When apologies emerge from an obsessive sense of guilt or shame, there is no real change in the quality of one's inner life. The blaming and murderousness remain, only now they are used with ourselves at the head of the target list. The wronged person may feel lobbied or threatened or forced to witness a ritual self-immolation. To stab yourself with horrible remorse is not giving; it's just another way of withdrawing, withholding, not being there. Authentic apology emerges from concern. And the same concern aroused in us for the person we have harmed can be available on our own behalf as well; there is a turn toward a more caring state.
What made Bill's apology especially moving was his ability to own up. Owning up means getting past one's defensiveness. It means stepping out of the blaming system, in which one person has to be not only wrong but the bad one, the unforgiven. Perhaps most important, the aggression is owned—we admit to feeling murderous—and, as a result, it becomes less overwhelming and controlling to the person it has been aimed at. We do things that are thoughtless, inconsiderate, selfish, mean, and we do them often in disguised ways. In almost every conflict, one or both of the people involved are covering something up, presenting themselves as cleaner than they really are, all the more so if blaming has been an important factor in their upbringing. This kind of behavior is very threatening. Someone is going to be it and feel deeply and unforgivably bad. To own up, to say something like "First I made a dumb mistake and then I blamed you for it," and to say it with caring, gives a lot, because it frees the other person from that badness.