Except N isn't trying to be better than you, his goals are completely unrelated to yours. He doesn't give a crap about the Pokemon League or Pokemon Training as a whole, in fact he hates what you stand for. He is in no way, shape, or form a "rival".
I don't consider N to be a rival anymore than I consider Giovanni to be a rival back in Gen 1.
But I don't necessarily think your rival just has to be the person with the starter strong against yours. For one that would eliminate "Gary" from Yellow as a Rival, and I also consider Bianca and Wally to be Rivals.
I was really disappointed by May/Brendan as a Rival though. I get that they ultimately decided they didn't want to be a Pokemon trainer, but they could have given us at least one fight where they had the final form of their starter.
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