No matter how impassioned the argument, there can be points on which mortal enemies agree. Ideas can't be generated when your only goal is to say NO louder than anybody else. But once you are no longer warring parties, but members of a team working together, ideas have a chance to get born. Now you can can brainstorm ideas, and look at how other people have dealt with your problem. You can bring in experts to answer your questions, and assign members of your team to research specific problems or possible solutions.
People deserve a chance to lose and still feel good about themselves.
I remember a theater professor at Northwestern directing Pygmalion in the final scene, when Henry Higgins had fully expected to bully Eliza Doolittle into coming home with him. When she stands up for herself, matching his jibes point for point, for the first time, he begins to see her as an equal, not as his eternal student. We don't think all that much alike, but he knows all kinds of things I don't, especially about economics and statistics, just as I know a lot of things he doesn't. We pool the best parts of each of our ideas, and make something better. It works because we respect each other.