Most conflicts can be resolved, but often we don't know how or we don't want to. We think we are proving a point but actually we are harming ourselves in the long run.
When triggered you carry an emotional charge.
It is this charge of energy e.g. anger that you feel against the other person who did something to you. When this happens you are in conflict with that person.
Should you let this charge of anger stay in your system, it will eventually lead to ill health so in fact you are hurting yourself more than you are hurting the other by not speaking to them.
In order to resolve the conflict and be the better person, have the discussion or write a letter to the person who made you angry. Perhaps they will apologise. Perhaps you can find it in your heart to forgive them. When you can do this and really let the charge out then you will have resolved your conflict. I guarantee you will feel a better person.