When trying to make peace with someone in your life, one of the key components, in my opinion, is that they hear not only your words, but what is in your heart behind the words. Unfortunately, that is not always the case and it impedes any progress that can be made.
Frequently, the emotions in a conversation become buried under the need to be right, the hurry to get out what you want to say, or absolute belief that you have been wronged. Anger raises a wall so high and so impenetrable that any other emotion is blocked.
To make progress in resolving a situation, all of the emotions have to be acknowledged. If your anger or pain will only allow negative emotions to permeate the environment; the love, caring, and true compassion fall by the wayside and are lost. Most situations, no matter how dire, still contain elements of those emotions and they are needed for resolution and peace.
Remember to hear and acknowledge all of the emotions. That is the only road to peace.