When you apologize, you should say "I am wrong. I did this (clearly explain what you did) I was at fault." When I was going to Overeaters Anonymous we used the Big Book of the AA. One big lesson that I learned that in any argument both parties were to confess or apologize for what they personally had done wrong. They were not to think about what the other person had done wrong,
Think about asking for forgiveness. Without using the word "forgive", how would you ask to be forgiven. When you are asking for forgiveness, what are you really asking for? It seems to me that when a persons asks for forgiveness, he is really asking, "Please pretend like I never hurt you. Don't hold any ill feelings towards me and treat me well. The purpose is so that I won't feel condemned by you and so that I can feel good about myself again."
In this prideful society it is so common to think only of oneself and what "I" want. Asking for forgiveness is a self-centered request. It is an act of asking to not be held accountable for one's wrongful actions. When you ask for forgiveness you are asking something from the offended party that she may not be ready to do.
True forgiveness follows a change in behavior of the offender that is demonstrated and proven over a long period of time. It may take months or years. True forgiveness is not an instant action.
If you have harmed someone, as much as you are able, repair the harm that you causes: repay what was taken, replace what was lost, repair what was damaged. If it will take a long time do accomplish, do it anyway. Do this with no expectation for applause. This is merely your duty and should be done because it is the right thing to do.
Jesus said to forgive. He did NOT say to ASK for forgiveness.
It doesn't matter who is right or wrong. It is your responsibility for fix the Disturbance. "Realizing that a disturbance is your responsibility is a giant step towards emotional maturity1." "Take full responsibility for the offense, without sharing the blame with anyone else, and without presenting mitigating circumstances"2