Holding resentments towards one's partner is common but what does one expect will happen?
Holding tightly to one's stance, "I'm right, he's wrong," gets you no where. Holding resentments is an action which hurts oneself, not the other.
Why do we do it then? What are our hopes? Does holding a resentment actually lead towards the change that a person desires?
Speaking honestly and openly with one's spouse is much more productive than being grounded in one's stance of being right.
Try being open, honest and vulnerable with your spouse about your feelings and thoughts on an issue. See if open communication can ensue this sparking intimate conversation and conflict resolution. Open, honest communication is more apt to get you what you want than pouting or holding a resentment.