I'm reading Peace at the moment - wonderful book; really inspires you to look within, you know? Challenge your perceptions of yourself and others.
Usually when we make mistakes out of anger, jealousy or hatred, we justify our actions. "Yes I did this or that, but only because I was angry at this thing or this person". We rarely "back down", and even when we know within ourselves that what we did was wrong, we can still find some justification for what we did, as view it as being right.
However, when we admit we are wrong, when we sincerely regret the actions that came from these negative emotions, we face ourselves. We take responsibility for ourselves and we hold ourselves accountable for our actions. As a result of this, we acknowledge the consequences, the harm our actions bring to others and ourselves. When we stop running away from the situation (i.e. justifying our actions), from there wisdom is born.
When people react badly to our confessions, we become frustrated or upset. Surely they should forgive us, right? That's not for us to expect. How they deal with you is their business, and if we have hurt people in some way, there's no guarantee that a confession/apology will bring a positive reaction.
But it's not about their reaction. You can't control how they feel, or what they think. However, by facing up to what you have done, by admitting your mistakes, you take the first step that many don't: you take ownership, responsibility for your actions and in doing this, you really learn to chip away at the negative actions and become more mindful of the consequences that your actions have - therefore, you eventually stop making the same or similar mistakes.
By not admitting mistakes, by not taking responsibility, how can we recognise that we are making mistakes? It's impossible to be wrong when you think you are right.
In the end, your practice is about your own self development, it's not about anyone else. Admitting your mistakes is not about getting forgiveness from others; it's about taking the steps necessary to wake up to yourself.
Hope this helps! (Moreso, I hope it's accurate...)