Really I believe all these rivalries are ridiculous and pointless. The most annoying one out of all these in my opinion would be a tie between Ash/Paul because of Paul always calling Ash pathetic and bullying him for no reason whatsoever, and Cilan/Burgandy because hearing Burgandy complain on and off about who's the better Connoisseur is just a waste of time, because obviously Cilan's much more skilled than she is.

I don't understand why this is even a rivarly to begin with. That is why I think it is pointless.

Well, I think the reason is Oshawott would always steal Pignite's food from him and then belch right in Pignite's face, and he wouldn't show any signs that he was sorry for his actions.