>I don't know if I agree that the best arguments result in agreement between opponents.

They don't end in agreement, they begin with cooperation; you might not resolve the argument, or your position might prevail, or even change. As you say, there is no argument to be had in some cases, there is no reason. I'm talking about a methodology, rather than an outcome; you can still disagree.

That said, in the case of something like the slave and their master, I'd suggest that an argument is pointless in any case; what's needed is a fight (in the literal sense).