One of the most famous sketches ever presented by Monty Python’s Flying Circus is the “Argument Clinic”, which at least for the time being you can watch in its entirety right here via the magic of YouTube!
The hapless customer in the sketch eventually leaves his argument session in dissatisfaction at the perceived lack of quality.
“This isn’t an argument!”
“Yes it is!”
“No, it isn’t, it’s just contradiction!”
“…No it isn’t.”
One wonders if he might have been better off seeing if they had a “Debate” category. In any case, it’s a good consideration for fiction writing where characters are going to have an argument. People just shouting yes, no, yes, no at one another gets old fast even in real life, much less in the realm of fiction where conservation of detail (and dialogue!) comes into play. On the other hand, if you get too fancy they’re going to sound less like people and more like talking points.
This is where it becomes vital to remember who’s involved and why they’re arguing, not just what they’re arguing about. Also important are the skills and “weapons” they bring into play. What’s an argument, after all, but another kind of fight scene? An uneducated character usually isn’t going to start eruditely quoting Aristotle in support of their views — that’s not a weapon in their arsenal. If there is, it’s usually a case of someone outside the fight “handing it to them” — say, some TV pundit they were watching — and even though they’re using it they won’t be particularly skilled and will be in danger of a swift parry and riposte by someone better trained. On the other hand, they may be stubborn enough not to care, or to possibly change the fight into something more actually physical. Which brings up another point: if someone’s physically superior, then you as the author have to figure out why they wouldn’t take advantage of that to get their way and instead are fighting a possibly losing battle in the realm of emotions and words.
As the author, it’s good to set the scene towards the outcome you need, but then I’d say “let them fight”. Let those debate points and insults and wheedlings fly from their lips according to the individual(s) in question, so that the conflict itself feels natural to the audience. If that leads down an unexpected path, then perhaps a reset (rewrite) is in order, or maybe your plot itself is what needs to give a little if the characters keep veering off script. And yes, that’s a weird concept considering you’re in process of writing the script. But you shouldn’t ever have to feel like your hammering your characters back into the shapes you demand, like they were so many nail heads sticking up from the otherwise smooth board of your story. It’s conflict, after all, and conflict by its very nature isn’t smooth. It might be better to work with the bumps.