If anything, I feel like it pretty much makes for a good ending point for an argument, if played out completely. If two people are working with the same set of facts, and understand eachother’s positions, and understand why the other person holds that position, but both still hold to their different views, then the difference probably comes down ultimately to different values, and since those aren’t something one is going to simply logically argue someone onto or out of, there is no point in continuing an argument after that.