If you try to make peace between two people who have been quarreling, don't take sides and tell one of the people that they are wrong and therefore should be the one to make peace. Since this person thinks that he is right and the other is wrong, he's likely to turn against you and quarrel with you!
A more effective approach is telling him: "Even though you believe you are totally right and the other person is totally wrong, you should still be the one who pursues peace. Take the initiative to approach the other person and apologize to him. Don't wait for him to apologize to you."
Today, think about two people you know who are quarreling and try using this method to bring peace between them
(see Rabbi Chaim of Volozhin - Ruach Chaim 1:12)