Have you ever been asked to "be the bigger person" after you've been in an argument with a friend or family member? Annoying as this may be to hear sometimes, the fact is every relationship needs someone to be the bigger person to help repair the inevitable ruptures that occur. This is especially true in parent-child relationships!
BUT, being the bigger person doesn't mean bottling up pain, apologising for your wrong and the other person's wrong, or suppressing your anger and acting like you are not really hurt.
Apologising just to 'make peace' when you don't want to, when you are still hurting and confused by what happened is not being the bigger person and doesn't help the relationship improve. Usually you feel more resentful, unheard and the pain builds up over time and eventually erupts either physically or mentally.