When I have a problem which falls into the irreconcilable category with another person, I have a process. Sometimes it can be a very LONG, drawn-out process, because there have been people in my past who have caused me great trauma. I have had to forgive them for my own sake, however, so I don't implode from internalizing the pain and anger I have felt from whatever caused us to part.
Let me explain my process: When something like this happens, I usually allow myself to feel the pain from it for a while. Sometimes a very long while. After a that while, I journal about everything I'm feeling at the time, and try to remember what I was feeling at the time of collapse. Sometimes, this stage will also take months, and many, many journals. After that, I ask myself if I want to try to fix things, or if I should just let the person go for good.
There have been times when after processing for a long time, I realize there may be a way to work things out. I'm not unreasonable, and I'm sure there have been a number of things that have also been my fault. But I tap into my common sense, and what boundary feels right to me... and let that sit for a while.
If I find peace in simply forgiving, that's what I do. Other times, I have to forgive, let go, and place a boundary that will mean I don't see that person again. Sometimes I even have to tell the person this, because they don't really understand what has happened. Tempting as it may be, I have learned to steer clear of name-calling, or doing things that would fuel their drama. Tempting as it may be, I won't engage them if this is the way they choose to handle it. This doesn't mean I have to re-hash the past, and go into a long, detailed account of why I don't want to see the person again. It just means that I have placed a boundary, and I expect them to respect it. And... how do I expect them to respect anything of mine, if I don't initiate respect in the first place?
There is a time and place for everything, including scrappiness... and yeah, this isn't one of those times.
Right now, as far as I'm concerned, I've forgiven most people. And forgiveness does not always mean a free pass back into my life.