I think it depends on the issue at hand.
I think it is rather arrogant to hold somewhat minor issues over someone elses head and not "forgive." It is not necessary.
If you forgive, to me it is the same as accepting an apology or correction of a wrong, and then not being angry anymore. You have to be OK with the situation to truly forgive, because you have gotten over it. It doesn't hurt anymore. But if you still hurt, then, it is definitely not a forgivable item unless the other party performs some kind of satisfying action to make those bad feelings go away.