So I was wondering if you could talk about the Kyle/cartman and batman/joker parallels because there is a LOT. Im considering doing my own analysis but I wanted to hear another perspective, if possible?
This is an Interesting topic.
I think it would be an understatement to call Cartman anything but an agent of chaos. The Joker believes that everyone around him is no different than himself, and he seeks to expose that. While Cartman doesn't really want to expose everyone for being just as bad as he is, as that would require admitting he is bad in the first place, that is still definitely a belief he holds deep down. With Joker this belief culminates into an obsession with Batman, someone who operates by a strict moral code, someone Joker believes is SO similar to him, whose attention he is constantly seeking while trying to get him to basically "admit" that they are the same by killing him. The Joker finds great amusement in his altercations with Batman. In a very similar way, which I'm sure you've already picked up, Cartman feels and behaves when it comes to Kyle. If there is on person in south park Cartman truly considers on his level it is Kyle. And in a similar vein to the Joker he find great amusement in his and Kyle's arguments.
Neither Batman nor the Joker can ever truly win against eachother tho. Due to their unchanging nature and beliefs they can never cross that bridge. The only way for Batman to truly beat the Joker is to kill him (aka become him), which goes against all his morals, and the Joker could never kill Batman.
“You just couldn’t let me go, could you? This is what happens when an unstoppable force meets an immovable object. You truly are incorruptible, aren’t you? You won’t kill me out of some misplaced sense of self-righteousness, and I won’t kill you because you’re just too much fun. I think you and I are destined to do this forever”, a quote of Jokers from the Dark Knight.
(This quote is literally such a good description for Cartman and Kyle overall)
Just like these two Kyle and Cartman can never truly win against eachother. Kyle could never let himself stoop down to Cartman's level, and Cartman even tho he has attempted to "kill Kyle" many times, could never truly do it for the fact that his life would just be dull without him around to fight with.
There is a good chunk of works that depict that relationship between Joker and Batman as "friendly" (take that with like a grain of salt) in a way. The very fact that Batman refuses to kill him, even going so far as continually saving The Joker. Essentially allowing him to roam free again and again, simply because he believes that there is something worth saving there.
“Do you understand? I don’t want to hurt you. I don’t want either of us to end up killing the other. But we’re running out of alternatives and we both know it”, Batman in The Killing Joke.
In a similar manner Kyle is continuously trying to see something good in Cartman, even against his better judgement. Constantly saving him from trouble, from a sense of moral obligation and maybe even one of genuine friendships. There is a part of Kyle that genuinely believes that Cartman can change.
The same comic ends with the two characters realizing that they can never truly trust eachother (told to us through a metaphor in a joke The Joker tells to Batman). They both start cackling at the ridiculousness of their situation, almost as if they were two friends having a laugh.
We are shown so many times in this show that Cartman and Kyle could be genuinely good friends, there are multiple instances of them acting so. But their antagonistic relationship towards eachother is something Kyle and Cartman can never manage to escape, even after 40 years they seem to regress at the first look they have of eachother. In a way that's similar to the Joker and Batman they need eachother. Their characters linger on each other. They justify eachothers existence by being eachothers narrative foils. Which kinda dooms them to a life of fighting.