I have tried many times in my life to FORCE someone to just accept defeat in arguments where there was no ambiguity on what the answer and course of action is, and most times it doesn't work out as intended. Sometimes it does, and you need to find the right finesse, but it can be difficult. If I enter an argument, I enter it with the expectation that there will be closure, there will be an end, and there will be a point where everyone shuts the fuck up and it's settled. No more discussion. No nothing. I despise open endedness when it doesn't need to be there. I want clear starts and clear finishes.
When someone keeps arguing, for the sake of arguing because they don't like the answer to it, I tend to get really mad regardless of what it is. Work, politics, even things with friends, etc. and I will attempt to halt it. I absolutely LOATHE and I mean REALLY loathe the kinds of individuals you pointed out in your OP. Over time though I've learned that sometimes you have to halt yourself as ultimately it is only you that you are in control over. What I normally do is restate the initial premise, state that I made my case, they made theirs, and there is a refusal to find middle ground or any reasonable agreement. It won't be reached so any discussion beyond it will not be of any use, and I exit. If I have the ability, I'll put a cork in their mouth as well.
Why to people do this? Some people just don't know how to stop, and enjoy having things open ended even if it is not a good thing. It absolutely boggles my mind, but they do exist and seem to work fine in their own methods. As for being unable to handle being wrong, I think it is much more common for someone to feel they are always right, and are utterly impervious to any reason or persuasion. These individuals, are best left alone when possible.