Averse Adept

There is a character who is good at something. Maybe it's skill, maybe it's talent. Maybe it's both. He or she isn’t just above average at it, he/she’s good at it, possibly even exceptional.

Unfortunately their prowess is only matched by how much they dislike exercising that prowess. Of course the plot will probably put them in a situation that forces them to do it anyways.

(current title may be a bit of a misnomer. They don't have to hate that what they are skilled at exists to qualify (although they can), they just have to hate doing it).

Contrast Giftedly Bad. Folks Desperately Looking for a Purpose In Life are prone to this trope, when their dreams don't align with their talent.

Anime and Manga

 * In Naruto, a story where most characters are trained in the lethal arts and more often than not are glorified Child Soldiers  and Professional Killers, there are individuals like Haku and Itachi who don't like killing despite (or arguably because) they are exceptionally good at it.
 * In Wizard's Soul - Koi no Seisen Manaka doesn’t like playing Wizard’s Soul to win. Playing without putting effort into winning isn’t that bad though. The reason she hates trying to win is . The reason Manaka enters a tournament is because her dad ruined her family's financial situation when he fell for a scam and she thought winning money in a tournament would get them out of it.
 * Miho Nishizumi in Girls und Panzer changes schools in order to get away from an school club activity that she's good at but no longer likes. However, in what looks like bad luck, her new school's Absurdly Powerful Student Council forces her to not only join the same club at the new school but also become the club's captain.

Literature

 * Erin from The Wandering Inn has astonished people with her feats of violence including killing a goblin chieftain 1v1 and single handedly wiping out a nest of shield spiders. Erin actively dislikes killing. Killing things that are really stupid like flies is fine though.

Visual Novels

 * The Danganronpa series is no stranger to students who ultimately dislike their Ultimate talents.
 * Trigger Happy Havoc has Leon Kuwada, the Ultimate Baseball Star. During Free Time Events, he mentions that he hates baseball and would rather pursue a career in music.

Western Animation

 * Downplayed in My Little Pony: Friendship Is Magic: the Cutie Mark Crusaders keep ignoring what they're good at (and could actually earn them their Cutie Marks and set the tone for their lives) in favour of trying out many other activities (which don't get them Cutie Marks).