Recently I had an exchange about conflict with an experienced communitarian who maintained that it was possible for conflicted parties to simply agree to stop brooding over unresolved past hurts, put it behind them, and start from scratch. I was gobsmacked that anyone could think that would work. In my 41 years of community living, I'd never seen that happen (In fact, I was thinking it was for more likely that protagonists would continue to scratch each others' eyes out).
The key piece of data in the last paragraph is that the parties were still brooding, and that it was leaking into current interactions. I accept that it's possible for a conflict to not resolve well when it occurs, yet both parties can independently work through it to the point of accepting partial responsibility for what went awry, and truly put it behind them. But I've never see that approach work when both parties were continuing to feed the monkey, keeping the negative stories alive. (Brooding works fine for hatching chickens, but not so well in people hoping to put conflict in the rear view mirror.)
How could this happen? It's not unusual for two parties who are deadlocked to view the other party as wholly at fault, and the stalemate exists mainly because both are too stubborn to admit their role in where things went south. In the worst cases, both sides may think that their actions were fully justified as a matter of high principle, and you can wait until hell freezes over before anyone makes a first move.
This is, in my experience, where outside help can often make a big difference. Both sides feel misunderstood and object strenuously to the assignment (by the other) of bad intent. Each is eager that their view of events be recognized by the other as a precondition to listening to the views of the other side, and the protagonists never get out of the starting gate.
The advantage that outside facilitators (or mediators) have is that they don't have a dog in the fight, and are thus well positioned to listen to everyone. (In the end, it won't matter who went first; only that both felt heard.) Further, if Person A is conflicted with Person B and there's low trust between them there's a tendency for Person A to be suspicious of Person B's motivation in asking about their experience (do they really want to know, or are they just looking for me to expose myself for further attack?).
After decades of witnessing and participating in conflicted group dynamics, I believe that the largest hurdle to overcome is admitting that you're stuck and being open to accepting offers of assistance. I believe that resistance is due to a number of factors, any combination of which may be in play:
a) Lack of clarity about whether you're stuck
When in the soup, it can be hard telling whether you're entrenched or just embattled—where a modest amount of additional effort might lead to a breakthrough. Hint: if you notice that one or both parties are starting to cycle through the same statements or stories, it's probably time to put the shovel down and quit trying to dig yourself out of the hole.
Many people (or groups) hold the view that either they don't get hooked by conflict (very much), or that they they're perfectly capable of working through it on their own. In that environment, admitting that you need help can be a serious blow to one's ego, and there's a tendency to suppress it.
For a number of us, admitting you need outside help can be like airing dirty laundry—something you'd rather do only in the privacy of your own backyard. Showing outsiders where you've stumbled might not match up well with your mission statement. (Remember that part where you told the world that you'd be a model of sustainable social dynamics and creative problem solving?)
d) Lack of history with conflict going well
Most of us have had precious few personal experiences of conflict work going well. Cooperative theory notwithstanding, it's not easy to gear up for the possibility of volcanic venting or no-holds-barred teeth gnashing if your belly is doing flip-flops.
The good news is that there a number of ways to approach conflict that can help you out of the ditch—but none of them are very effective if can't admit that you're off the road when you up to your knees in ditch water.