It is well established is South Park cannon that Cartman is slightly obsessed with Kyle. Cartman also demonstrates a large number of trates that lead us to believe he is gay - watch the episodes, there are so many it would take a week of watching back episodes to list them all. For Kyman fans there is no need to strech the imagination to see Cartman liking Kyle - what is not obvious is why Kyman fans think Kyle could possibly return the Fat-asses feelings. Here are some of my thoughts on the matter.
First Possible Explanation
A lot of men tend to like a girl who reminds them of their mother in some way. With gay men the same trait leads them to look for a particular type of guy. Lets compare Shelia Broflovski and Eric Cartman:
1- Both are of a similar body type and shape (fat).
2- Both are loud and obnoxious with take-charge personality types.
3- Both tend to shreak and shout when they can't have their own way.
4- Both get obsessed with their schemes and take them way too far (e.g. Shelia being resonsable for the USA/Canada war in the movie, Cartman's revenge on Scott Tennorman).
5- Both have immense levels of overwhelming confidence.
The idea being that if Kyle was gay he would subconsiously choose a partner that would remind him of his mother. Cartman fits this mold nicely.
Second Possible Explanation
Kyle is somebody who will always look for the good in a person. If Cartman ever opened up the Kyle about his life and feelings - maybe Kyle would grow to like, trust and eventually love Eric. I wrote a story with this as one of the themes called The Contest: www.fanfiction.net/s/6082998/1…
Third Possible Explanation
Cartman manipulates Kyle into falling for him.
Forth Possible Explanation
Cartman matures/mellows out/changes as he gets older.
There are other explanations - some of which would make excellent stories.
Kyman love to all, Cell12.