Debate is a game. It's something most people don't quite understand, or don't apply.
If you're in a disagreement and you don't want it to turn into a fight, you both need to move towards treating the discussion as a debate, which is a game. That can be difficult, especially for a big issue, but if you can't, it's best to put the discussion aside for now.
Let me bring in a pretty typical definition of game. A game is a finite contest with rules, an experience you can win or lose, but the consequences are negotiable.
Russian Roulette has rules: put one bullet in a revolver, spin the thing, point the gun at your head, and pull the trigger. If it was a live chamber, you're probably instantly dead, and you've lost. If it was a blissfully empty chamber, you've won. But see, the consequences are not negotiable: either you're dead or you're alive at the end. So while Russian Roulette resembles a game, it is not.
Debate, on the other hand, is a game.
Many people very understandably don't want a discussion to be just hot air—they want to get something done with it—and by driving at that purpose too hard, they lose the value of discussion.
The value of discussion is that it's virtual. The words are only words. Your debate is a little virtual world of words, where you're trying to follow the rules of logic and evidence—you want the debate to have bearing on actual life. Yet the consequences of the debate are very much negotiable. What does it mean to win or lose a debate? Maybe nothing. Maybe something. That's all TBD by the participants afterwards. Nothing is set in stone. And, as I said, that is the actual value of debate. If you had to move all the bricks physically into different arrangements while debating architectural choices, civilization would still be in the stone age today.
The virtuality of conversation, and debate, is its greatest strength. And then people go and forget that, or never quite understand it and its implications.
Some people understand debate is a game, whether they would use that word or not. And they are usually much more pleasant and engaging to discuss controversial topics with. This doesn't mean they have no beliefs or don't consider the topics important, or even critical. It's just that debate is a game. You don't solve global poverty in your chit-chat with your housemate over dinner. So stop acting like you do, and if you have a particularly good round of debate, you might actually be somewhere at the end that you weren't at the beginning.
That's how it works, and it really truly does work.
* Note: just because it's a game doesn't mean you have to be goofy, though that's often a very useful approach. Taking the pressure off allows people to speak more freely and think more creatively together. But you can also be very serious. Debate that's a game can still get heated, but it never gets personal. The feminist "everyone's perspective is valid" approach is also a great way to make a debate a game. Goofy, spirited but not personal, listening while perspective-taking—all of these are ways to make debate do its job, and they share the same principle. To the extent they would ever get a little intense or combative, everyone understands that this is sparring, and nothing to do with liking or disliking each other. May the best idea win.
** The definition of game and the Russian Roulette example I'm pretty sure both come from the book Half-Real. My copy went to a good friend 6 years ago before I went into a big surgery I thought I might not survive (statistically, there was a 1% chance I wouldn't, which makes a very big and relatively safe revolver for Russian Roulette, but that's a smaller revolver than for most surgeries, and it was a 5 hour procedure that left me with 55 staples and now a 13-inch scar, so maybe I wasn't being that dramatic). I hadn't finished reading it, but it has the best definition of game I've ever seen anywhere, by a long shot. Most books on game studies start out defining game (yawn). This one, though, makes that triply worth your while to read.