Words have power. You can get metaphysical, spiritual, or just commonsensical with it. When you tell yourself you will do something, you usually do it. When you say, "I think I'm getting sick" you usually end up sneezing within the hour. Words carry the ability to shape your world. We let what people say to us shape our opinions of the world around us and sometimes our opinions of ourselves.
If someone says to you "Oooo girl you are getting fat". You start sucking in your stomach and skipping dessert. If someone says, "You look good in that color" you go buy five dresses, a scarf, and two pairs of shoes in shimmering clown lilac. Recently I got caught in the rain so I had my shoulder wrap over my head with my sunglasses on under the clouds. I felt awful and knew I looked horrible. UNTIL...I passed a young woman who whispered to her mate, "OMG! She looks fabulous". Miraculously, I felt fabulous and morphed from soggy to sassy. Words have power.
So why is it when someone says, "I'm sorry" we are unmoved. We've all told people that actions speak louder than words. When it comes to apologies most of us migrate to Missouri...Show Me! A friend or mate can say the most hurtful thing that has the power to hurt your heart forever, but five minutes later when they say "I'm sorry" the words are completely powerless. I am strictly speaking of apologies that follow words. If I find you in the bed with the babysitter or find out that the babysitter is your baby then your words move to flyweight status-weak . But if you "say" something hurtful and then "say" you're sorry, why can't we accept that just as easily as we accepted the former?
I think I have come to a conclusion. It's not earth changing rocket science nor does it slide into the depths of Freud's psychology. The reason your apology isn't as powerful as as your verbal assault is because I don't believe you. If I did, it would be more powerful than your initial comments. In the same way your assault wouldn't have affected me if I didn't in some way believe it were true.
The actual power is not in the words. It is in my belief of the words. So when say you're sorry, make me believe it.