Its been stated its not going to be simple A rivals B and B rivals A
Its a long chain
A is rivals with B when you play A's story line
B is rivals with C when you play B's story line
and its just a long chain going down until it comes in a full resolution where Z is rivals with A in Z's story line
I dont know why people are having such a hard time understanding this, having A rivals with B and B rivals with A would make it rather dull, because when you play both A and B's stories, you're going to have the exact same cutscene at the end. This chain gives us a lot more characters interacting with each other and a lot more different cutscenes at the end of the character's arcade mode.