>>48481867You didn't read the manga at all. The very reason why Yvonne admires and respects X is because their roles were reversed when they were kids: she was the one with self-esteem issues and insecurities, X was very cheerful and outgoing. He inspired her to pursue her own dreams instead of just being Grace 2.0. It is implied that Y was very depressive because of her mother's heavily strict training, she constantly fought with Grace about not wanting to be a Rhyhorn racer, one could even argue Grace abused her emotionally.
Later on, X became famous because of his talent for pokémon battles. He then became a shut in because he couldn't handle all the harassment from the media at his short age. He had no privacy at all. That's when the new and improved Y steps in as a source of emotional support for her friend. However, her attempts to get him out of home weren't really that succesful. Shauna even comments on how Y was getting frustrated of this situation, even implying that she was about give up and leave X on his own. Had the events of the first chapter not happened, they probably could have become estranged
The very reason why X's gratefulness towards Y at end of their adventures is so significant is because it means her efforts were not in vain.