Despite context being provided for instances of Cartman saving Kyle, as well as many actions Cartman has taken against Kyle due to hatred, there still is a subgroup in the South Park fan base that strongly believes otherwise.
My question is: Is there any substantial evidence, not theoretical, that may back up claims of Cartman sincerely caring for or having deeper feelings for Kyle?
Similar to BCdotWEB, I'm a bit on the fence of whether there's an underlying valid question. However, you stipulated what part you specifically want an answer on:
Why do some people believe Cartman genuinely cares for Kyle?
It's a question in the sense that I want an answer as to why people think that, something that in a way might rebuttal what I've said
The short answer is this:
Because there have been instances where Cartman did something for Kyle that came from a place of wanting to help a friend. These kind moments also help prove that Cartman's usual hurtful comments are not the literal truth.
As much as Cartman can rip on Kyle and say that he wants him to die; at the end of the day, he chose to save Kyle in Smug Alert. That indirectly proves that he doesn't hate Kyle as much as he claims he does.
Yes, you're somewhat correct that this kind gesture is tainted by the fact Cartman misses Kyle as his favorite victim, not just as a friend.
However, it does still prove the point that Cartman's usual hateful anti-Kyle rhetoric is not true to begin with. It showcases the point that when Cartman rips on Kyle, he's exaggerating.
This ties into a larger part of Cartman's personality. Cartman has hateful opinions about certain groups of people (Jews, hippies, ...). But when you observe Cartman over all of the seasons, you start to see that his bark is much worse than his bite.
Cartman has learned to act offended when it helps him get what he wants. Cartman doesn't hate for hate's sake, he acts hateful because it benefits his true goal.
When Cartman wore the "Token's Life Matters" T-shirt, he wasn't trying to bring focus to racial issues. He was trying to bring focus to the fact that he is standing up to racial issues. Cartman's goal was self-aggrandizement; not social change.
In "Kenny Dies", Cartman attempts to get stem cell research (using aborted fetuses) legalized in a feigned attempt to save Kenny's life. It is revealed at the end of the episode he really wanted to use stem cells to clone his favorite pizza restaurant.
In "Ginger Cow", Cartman actually proves my point by completely pulling a 180 when it benefits him. Initially, Cartman keeps up the prank that the ginger cow is real. When confronted with an outraged Kyle, the school, the media... Cartman holds to the claim that the cow is real.
But then, peace in the Middle East is created specifically because the ginger cow is thought to be real. Cartman suddenly feels the need to come clean, but he confides that in Kyle, specifically. It's not all that subtle that what Cartman really wants is to extort Kyle, by making Kyle his servant in exchange for not revealing that the cow is a fake.
Cartman's actions change based on what benefits Cartman the most.
He first upheld the lie for personal amusement. He was enjoying it way too much to give up on it. But when he realized that he could instead extort Kyle (which would bring him even more joy), he changed his position so it helped him get what he wants (Kyle's reluctant obedience).
When Cartman victimizes Kyle, this is nothing more than a power play. Cartman wants to conversationally drag Kyle through the mud and retain social control over him.
As Cartman's advocate, I could argue that Kyle has a different-but-similar need for social control over his friends. Kyle is the one who most likes sitting on his moral high horse and behaves like the bringer of wisdom, even if others (sometimes including Stan) get tired of Kyle's harping on.
In that sense, Kyle and Cartman's treatment of each other is balanced. Kyle gets to act morally high and mighty (which most commonly consists of explaining why Cartman is being a dick), and Cartman gets to drag Kyle down and ridicule him (by trolling him).
Cartman and Kyle are two extremes at opposite ends. Based on a given topic, we can usually already predict what Cartman and Kyle's opinions are going to be. But Stan is the wildcard, and the more interesting character to observe. His opinion is not set in stone. He evaluates things independently and then makes his own choice.
Just to not exclude him: Kenny generally swings the same way as Stan; he picks a side based on the options in front of him.
However, if the plot requires the boys to split off in two teams of two each, since Kyle and Cartman are practically always on opposing teams; Stan and Kenny divide themselves to even out the groups. Most often, Kenny and Cartman group up, because Kenny has a "naughty" side to him that connects with Cartman's amorality.
Come to think of it, Kenny actually proves the point. Especially in earlier episodes, Cartman ripped on Kenny (for being poor) as much as he did on Kyle (for being a Jew).
But Cartman still likes Kenny at the same time. They often pair up. They genuinely have fun together. But when Cartman takes a joke too far, Kenny can (and will) lash out at Cartman. Kenny does have a thicker skin than Kyle, he doesn't get upset as easily.
Essentially, Kyle is a more sensitive Kenny. And because he's more sensitive, it's easier for Cartman to upset him, which is why we see Cartman/Kyle rivalry more than Cartman/Kenny rivalry (Kenny has no issues just walking away if he's fed up).
After thinking it over for a while, I finally have an answer: Is there any substantial evidence, not theoritical, to prove Cartman secretly cares for Kyle or sees him in a romantic light? No- however, there is evidence to back up a very clear fixation- a fixation that has led to others such as the groups above theorizing his feelings to be something...more.
Cartman, as we know, has the tendency to remain determined in the face of something he desires, and him hating Kyle is no exception to this. This hatred has culminated into a very strong desire to get one up on his rival and feel superior, which can lead to Cartman going through...questionable means in order to humiliate his enemy. A good example of this is the three parter Imagination Land, one where Cartman dedicates his time to making sure Kyle sucks his balls, as their previously made bet had stated. There's a lot to be said on the topic of Cartman and sexuality- it's implied during the course of the series that Cartman views sexual instances as a means to demean and humiliate rather than anything intimate as most would. Regardless of motives or not, the sexual implications of it are clear, and contribute to the theories. Another episode, one that basically defines the source of Cartman's fixation with Kyle, is Smug Alert. It provides the basis as to why, despite hating his rival, Cartman most certainly needs him. Kyle provides angry and overblown outbursts in response to Cartman's bullying. These reactions provide negative attention that not only sustain Cartman's narcissism, but his sadisim as well. This desire for entertainment is a bigger priority than his hatred, and so in turn Cartman saves Kyle. Now although certainly a selfish reason, this does prove without a doubt that Cartman needs Kyle around.
While there are many rivalries in media, very few contain the intensity and fixation that Cartman and Kyle's dynamic have, despite being just a sitcom. This, coupled with the implications of episodes such as Imagination Land, are enough to have plenty theorizing about the two.
