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i liked Kris so much more than lyra because Lyra looks and acts like a 5th grader getting ready for a picnic, maybe play tag with her pals or something.
Kris on the other hand, everything from her clothes to the stance she has says serious pokemon trainer.
She's literally a female pokemon trainer, that's what they made her as.
she's not some childhood "BFFL" or some other heavily backstoried bullcrap, she and gold were just 2 kids starting a pokemon adventure and grew from there.
i know this could be said about a lot of others, but really i like kris because she didn't need the other parts of the backstory. You watched her grow from a random trainer starting her adventure to a champion hero across 2 regions.
Kris will always be the best female trainer IMO, even if nintendo ignores/forgets her.