When it comes to conflict, most RPGs have entire sections of the book detailed towards resolving it. There are lengthy and intricate rules to decide how combat works with various maneuvers the players can employ, and various rules for how those various maneuvers work. However, this same attention to detail falls flat in other aspects of the game, especially when it comes to social interaction. I want to talk about that today.
Charisma is a Dump Stat
The problem this lack of detail can bring up is also the reason why many people (especially those not playing sorcerors, bards, or paladins) use charisma as a dump stat. Most social engagements are role played out, not rolled out and so the players - often rightly - feel that it is ok to skimp on social skills for their character because they can simply make up for this weakness with their play. Also, while many GMs are perfectly fine with letting an entire adventure be ruined with a failed combat (often meaning a TPK,) I've found very few who will let a failed conversation bring the adventure to a weird stall. Honestly, I can't even blame that view. It would suck and doesn't sound very fun...but why not?
There Are No Social Hit Points
One of the arguments I've heard against a combat like system for social is that while we have something (similar) to hit points in how our bodies work, the same isn't true mentally. To which I must whole heartedly disagree. A person is able to deal with less crap before snapping when they've had a bad day. A person is more suggestable to certain actions when they've had certain things happen. Sure, we may recover faster from these things, and some people can do a good job of keeping how they deal with different people compartmentalized, but some people heal faster than others to - and we do have rules for that.
A Question of Focus
The real reason I think this happens is a question of focus. Most people - or at least most designers - are building their games with the idea being to focus on combat. Maybe they want the action movie feel, or maybe they want the classic fantasy adventure. Heck, maybe it is just what they want for some reason. Either way, if the game is focused on one aspect, then it should cover that aspect better than others. Which also means that a game would have to want to focus on the social - at least for some characters - to have these rules.
But Does It Have To Be Different?
The question then is, how do you make rules for an argument? Well, I'd say they don't have to be all that different from combat. John Wick made a game where the primary focus was on sex, with people winning power over others by having sex with them. It isn't a bad game, and the system used for winning the "sex fights" could just as easily work for real combat, or dancing, or even arguing.
Aside from Sexcraft, the only other game I know of with detailed rules for social combat is 'Sufficiently Advanced.' SA is a great game (disclaimer: I know/knew the developer) and even comes with a chart for handling escalation in situations so that a GM can easily tell what takes resolution priority between a baseball game, an argument, a cutting remark, and a thrown punch. Definitely worth a look, and one of those games where losing an argument can kill you (0 social HP means you can be convinced to commit suicide)