Question: I have this idea in my head that I will only be able to forgive the ex who cheated on me if he owns up to his mistake: not in terms of the cheating, but in terms of how he fled the scene and didn't want to give me the time of day to break up in person. It's also important to note that he didn't admit to cheating - I found out from a friend.
I've already come to realizations about how we were incompatible as partners, and I don't want him back. I think I just want the satisfaction that he feels bad for treating a person so disrespectfully. If I have to accept that he will never reach out and show remorse, how do I move on and forgive?
Answer: Imagine that you could forgive him only if . . . he went to work in a banana suit. If he gave himself a handlebar mustache with a Sharpie. If he checked in at the next 20 restaurants he patronizes with "Obnoxious Jerk, party of 1."
Seriously - imagine these, or whatever other absurdity comes to mind, not merely to amuse yourself, but to drive home to the idea-making part of your head that you can no more make him own up to his disrespect than you can make him run naked through rush-hour traffic.
It's just a tendency of our brains to make a connection between what we think should happen and what is possible - when no such connection exists. At all. Any shoulds you believe in reside with you; any actions he takes reside with him. End of story.
So let absurd hypotheticals drive that story home. This exercise of distinguishing your jurisdiction from his can also help you with the question of how to "move on and forgive": Direct yourself to consider only what is available to you on your side of the line.
You can, for example, come up with an understanding of his behavior that feels less personally insulting, such as, "He faced temptation as we all do, and this time, it exposed him as weak." Or you can acknowledge where you're drawing conclusions without enough facts - maybe, "A failure to express remorse is not the same as a failure to feel remorse." Indeed, he could feel bad about his actions but lacks the courage to say so. Maybe, too, he thinks - mistakenly, of course - that apologizing would be a selfish attempt to ease his conscience, that, therefore, the kind thing is to leave you alone. It's not an uncommon (mis)calculation to make.
Or you can leave him mostly out of it and concentrate your mental dialogue on forgiving yourself - for picking the wrong guy, for missing signs that all wasn't well, for not fully embracing up front that having real feelings for real people is a messy business, that disappointments are inevitable - and that some slap us harder than others. Or just forgive yourself for caring so much, since it's better than the alternative.
Find what sits right with you and then, when you're ready, make it all the reason you need to consider the matter closed. Not painless, just closed.