If you really can't understand despite the overwhelming evidence being tossed your way, look at Cartman's responses/actions. Did he ever show a hint of wanting Kyle back due to Kyle being his friend, or missing other characteristics of him besides his over blown reactions?
No, he didn't. He only began to miss Kyle after Butters proved to be a boring replacement.
C- "I guess you Heebs can't even play video football!"
B-"haha, yeah, you're right."
C-"You know Butters, you make for a lousy Jew.'
This is the start of Cartman missing Kyle (or rather his reactions). Is there any other action that shows Cartman missing Kyle for a reason other than his entertainment value? No, because there's actually none. If you have a rebuttal to this and what I said above, I'd really like to hear it.