1) For me, it is kind of funny that (in this game) one team is a rival of another, but not the other way around.
Your examples proves that it isn't so in the real world.
2) A team can have few teams as their rival, and not just a single team like it is in the game.
This means that it was meant to be - one rival per team, both ways...
3) In the "real game", a better team has more rivals than those who aren't.
A team that is longer in a league, will "acquire" more rivals during the years.
This 3rd point is more of a suggestion...