Consider a verbal fight within a couple. Everyone wants to have the last word and both throw loudly anything they can come up with at each other. In such a situaiton you may be able to break that mental stance of your opponent by "simply" shifting the topic/perspective to something, they did not expect at all. This way, you may be able to force you opponent to give up the trench they dig themself into.
I know its not simple. This is more education than superficial conversation.
I find the best tactic in this situation is to let the other party exhaust themselves. You're never going to be heard, so just listen (actually listen, not pretend) until they've got whatever they want to say out, and then make a response that shows you've listened and tried to understand.
When a conversation is stagnating in a cycle and you elevate it on a meta level, away from the original topic to that conversation and how it is going, you will not only display good faith but you may be able to find the traces of good faith in your opponent and maybe turn back to the original topic.
You cannot flip the table and still call it a game. Its not a game move when your intention is progress and not a rhetorical win.
I personally use the meta-conversational move a lot, and it usually turns heated political discussions into more thoughtful philosophy discussions. I think because most people don't have such strong identity based beliefs around questions like "how can we know if something is right/true/good/bad, what does that mean?"
The meta-conversation technique blew up for me once. A buddy and I got into it and I went in that direction of how do we know if something is good or bad, right or wrong, and it had him feeling incredibly frustrated and distraught, questioning whether his friends have fundamentally different values than he does. I recognized in that moment he seemed very emotionally vulnerable and so I switched out of my head exploration and opened up deep abkut some of the emotional struggles I had been facing. I think very often conflicts are not about the actual conflict we discuss, but about tangential, or even unrelated, things.
That actually sounds like a true philosophical situation, where you both questioned some deeply held beliefs. This can have epistemologically and existential repercussions for the individual, especially if you are emotionally invested (and we always are at some level)
Perhaps, I'll think about that a bit more. I think I was seeing it more as me using theorizing as a defense mechanism to avoid opening up emotionally and connecting with my friend on a deeper level. I've noticed in my life that I can often dive deeper into theory, hypothetical situations, and general philosophy as way to distance myself from how I'm actually feeling in the moment and from saying that to others.
Oh yea, as a general rule of thumb I have found that if any party is getting emotional (defensive, frustrated, hurt, etc) then the conversation will have to pivot to feelings.. something about the pre-frontal cortex going offline when we get into a certain state.
I've seen this state called different things, like "Exiles" in IFS therapy, "below the line", "tilted", "triggering painful spots", I usually call it "defensive".
(Aside... a thing I've learned is not to ask if someone is feeling defensive (if they are, they'll say no). Instead I think the better move is to ask if they feel like I'm not listening, or not understanding their position. This lines up with the internal thoughts of feeling defensive.)
All this to say, rational conversation is possible when two people are in a rational state but there are other states of being.
(Aside.. I find that rational communication techniques like NVC are actually devilishly hard to put into practice all the time because they go out the window when we get tilted.)
(Aside... EFT couples therapy is designed around communication in an emotionally vulnerable state as opposed to rational, and supposedly has pretty good empirical results)
Consider a verbal fight within a couple. Everyone wants to have the last word and both throw loudly anything they can come up with at each other. In such a situaiton you may be able to break that mental stance of your opponent by "simply" shifting the topic/perspective to something, they did not expect at all. This way, you may be able to force you opponent to give up the trench they dig themself into.
I know its not simple. This is more education than superficial conversation.