This is not about right or wrong. What Peter was negotiating for was a bigger piece of the pie, maybe even another song on the tour. Although I don't know what was in those negotiations, it was clear that Peter was asking for more than Gene and Paul could give. I also believe that both sides have well-paid advisors that tell them what they should do. The result was that an agreement could not be made.
Nobody hates each other.
It just became a situation that didn't resolve itself in time for the next tour. And that's why Eric Singer is involved. This is not about spite. It's about promoters, contractual obligations, and money spent on the upcoming shows in Japan and Australia. You can't cancel at this point without money being lost and lawsuits flying.