One-sided rivalries is basically a term where two cartoon or anime characters have a rivalry, but when they battle (or compete or dance or whatever the case is), one person of the rivalry always defeats them in said battle.
Bob: What, Dan?
Dan: That in that one anime-what's it called-Azumanga Daioh, Sakaki always wins against that other girl...Kagura I believe?
Bob: That's a one-sided rivalry, Dan.
Dan: So that's the term. And now I know.
Bob: And knowing is half the battle.