We all value different things! This is the basis of most personality analysis programs, to recognize what we value, what we expect of others, what we are willing to offer others, and what we don't want. The Enneagram is one tool that can help us clarify and understand what we find important, what annoys us the most, and what we are willing to do about it. Another similar tool is Gary Chapman's "Love Languages", which help pinpoint what we like and expect of our relationships, and what we do not care about. In the real world of conflict, I think there are at least three things going on.
One is the content of the disagreement or hard feelings--what was said or not said/done or not done that set off the reaction. Often it is not clear or not understood why someone took offense at something that happened (or didn't happen), and someone else didn't see why it was important. Chapman describes five things that can be easily misunderstood in a relationship: the value of words, works, things, time and touch. In addition to whatever triggered the conflict, people have different ways of expressing their displeasure. Some people yell, some people clam up, some sulk, some leave the scene, some nag. Some people won't explain why they are angry, some people tell everybody.
Then if you recognize what is happening, there is the opportunity to do something about it. If you're ready to settle, compromise is a Good Thing. An apology and asking forgiveness can be a growth experience. Agreeing to drop it is another possibility, especially if there is the commitment to actually let it die and not dig it up when somebody's being crabby. Some things can't be fixed, and have to be lived with (and hopefully learned from.) What is not pleasing to God is letting them simmer on the back of your life forever; this can become a generational cold prickly thing and take the joy out of your life. A grudge can poison your relationships for a long time.
What I have learned is obvious, but we don't always think of it. Prayer is a great healer! And I don't mean telling God how horrible someone is, but shut up and listen for His wisdom. He can give the strength to deal with the tough stuff, and the grace to let it die. He really is smarter than we sometimes give Him credit for!