A debate has usually stopped being productive when you are no longer examining the same claim. The conversation starts looping, goalposts move, old points are repeated, or one side refuses to acknowledge facts that have already been established. Personal attacks are another clue. Once the focus shifts from the idea to the person, you are often no longer evaluating anything. You are just fighting.
Another warning sign is that neither person is willing to update. Good debate requires at least some possibility that evidence, logic, or clarification could change your mind. If every answer simply creates another objection, or every fact is dismissed because it came from the “wrong” source, there may be nothing left to evaluate. At that point, continuing usually adds heat without adding understanding.
When that happens, exit cleanly. You can also say,
“I don’t think we’re getting anywhere, so I’m going to leave it here.”
I personally don’t favor that approach. It fails to pivot toward the relationship.
A common approach is to summarize where you agree, state where you still disagree, and stop without trying to land one final punch. Something as simple as,
“I think we understand each other’s positions, we just disagree, and that’s okay.”
That works surprisingly well.
My dad’s advice was to change the subject. You can simply say,
“I’d like to stop now, how about we take a break from this, and talk about x.”
That’s my favorite because it frequently brings humanity back into the dialogue. When I can remember to do it, it has worked well. A good exit should protect the relationship and keep the door open for a better conversation later.