What about if they don't let you discuss the issue? How do you resolve the conflict then? Do you give up and move on?
I'll let them know that I'm hear to talk if they ever want to and that I do care about how they feel. We both entered into a relationship because we obviously felt something for each other and perhaps things changed since then, but I still care about everything, even if things don't work out. I'll try my best to put my emotions aside and not be confrontational .. and let them know that I just want to talk about how I feel and about how they feel, regardless of who is right or wrong or more right or more wrong. I don't know where we'll go from here but I just want to talk about it and try and understand why things ended up how they are.
It's easier said than done .. especially if I'm really angry, but it's what I try to do, at least once I've had some time.
Usually, I've found that if I'm not accusing and emphasize just wanting to discuss it, over time, people are willing to talk. I try to do more of the "It upset me when ___"s rather than "You ___"s. Chances are if it hurt me, it also hurt them.
And, if they're really insistent on just never speaking again... I'll leave it alone and respect their decision. But, I'll let them know that I appreciate everything they did, that I'll always be up for a conversation, and that I'm sorry for whatever wrongs I may have done. I show them I care, but I can't have a one-sided conversation with someone completely bent on not saying a word to me.