Accept Responsibility

Think about if having the upper hand is more important than having this person in your life. Every situation has two sides to the story, and every broken relationship has two people at fault, so accept that you are also partially responsible for what has happened. This will help keep you from transferring the blame onto the other person, and therefore be more open to apologizing. Opening yourself up will encourage the other person to let go of their own ego and do the same as well.