>>149321120
Ok but I'll give you the short one too first: Kyle likes Cartman's company and feels fond of him.
Now, onto the why. Kyle and Cartman are written as pretty much opposites in many ways, but they have a lot in common, they're two sides of the same coin and the show itself lets you know on multiple occasions that they enjoy each other's company. Their interactions may seem like fights on the surface but they are actually mutually beneficial. Kyle gets his ego stroked by being able to place himself as morally superior (due to his martyr complex, something we have seen in Ginger Cow for example), while having an outlet to let out anger in a justified way (especially considering the pressure he is under by his strict mom or sometimes his parents in general). On top of that, Kyle genuinely has a thing for leading (usually a girl) someone helpless to safety and helping them. He followed the same MO with Leslie and Heidi, but generally if Cartman is in trouble he'll do it with him too. On the flipside, Cartman feels the need to have someone that provides structure and pushback since everyone else gives into him, he looks up to Kyle for his morals (and his status) and he knows that Kyle would help him, so even when he doesn't do it, Cartman still feels fond of him. He also has this need to try to bring him down to his own level, probably due to his insecurities. Because of this delicate balance, they're always trying to one up each other by getting to have something the other doesn't, but due to their underlying motives for interacting, they stay friends anyway. Even better, they help each other without wanting anything in return (smug alert / jewpacabra).
I'm sure there's more I could say about it but off the top of my head this is good enough.