Rivalry

Especially common in Japanese fiction. Often used as comedic element with one character claiming the protagonist is their rival and then try to defeat them in more or less friendly manner in whatever they're supposedly rivals in (perhaps most commonly failed sabotage attempts on the protagonist). If the protagonist is the one claiming the rivalry, the comedy is commonly exchanged for more serious challenges for the protagonist that they likely eventually overcome and gain the respect or admiration of the person they chose to declare their rival.