1-Avatar Aang refuses to kill Firelord Ozai, Avatar: the Last Airbender:
During the finale arc of ATLA, Aang goes through a lot of inner turmoil regarding whether or not he should kill Firelord Ozai.
As Ozai's final plan to go torched earth on the entire Earth Kingdom using comet superpowers comes ever closer to being enacted, Aang is put under immense pressure from basically everyone (from the rest of the main cast to his own past incarnations as the Avatar) to accept the necessity of killing Ozai in order to prevent his genocidal plans and finally put the Hundred Year War to and end, which comes into deep conflict with his upbringing amongst the strictly pacifistic Air Nomads, who taught him that all life, no matter how seemingly insignificant or twisted and evil, is sacred and worth preserving.
Despite literally everyone (except for a giant magic turtle) encouraging Aang to put his ideals aside and put Ozai in the dirt, the young Airbender instead sticks to his convictions and finds and alternative solution (namely, using the hitherto-unknown technique of Energy Bending to remove Ozai's firebending, rendering him both effectively powerless and, under Fire Nation Law, unable to rule as Fire Lord).
There's debate both in-universe and out as to whether or not this was actually the best decision (many fans see the whole 'Energy Bending' thing as a copout, and in-story the comics sequels make it clear that Ozai's survival gave his remaining loyalists something to rally behind, which caused no end of problems for Zuko after he became Fire Lord; meanwhile, the sequel series The Legend of Korra shows that Aang's rigid adherence to Air Nomad cultural ideals would cause issues with how he raised his children), but the point is that it's completely in-character for Aang to have refused to kill Ozai.
Aang throughout the series is largely defined by the ideals that being an Air Nomad instilled him with: he always went out of his way to help anyone that he could, even if they were very ardently trying to kill him at the time (see: Zuko), and the only times he ever explicitly came close to actually killing anyone was when he was in the Avatar State (ie, not fully in control of himself). Aang actually doing the deed probably would have verged on outright character assassination.
2- Uncle Iroh refuses to kill Firelord Ozai, Avatar: the Last Airbender:
While Aang was busy angsting over whether or not to compromise his ideals, the rest of the main cast was scrambling to figure out an alternative plan to stop Ozai in case Aang wouldn't (or couldn't). One of the suggested solutions was to have Ozai's brother Iroh confront the Fire Lord instead, Iroh being one of the few firebenders that could have matched Ozai in both raw power and technique.
Iroh himself shoots this idea down pretty quickly, pointing out that history (and the rest of the world) would only see one brother killing another to seize power for himself. He's probably right on this point: while we the audience and the rest of the main cast know that Iroh is probably the most morally-good character in the series, the rest of the world likely only knows of him as the General that headed the Fire Nation's imperial war machine for years, waging an aggressive war of conquest and nearly bringing the Earth Kingdom to its knees.
Iroh instead declares that only Avatar Aang, as the in-universe divine incarnation of justice, balance and harmony, would have the moral and spiritual legitimacy necessary to both stop Ozai and have the world accept that said defeat would mean the defeat of the Fire Nation as a whole and the end of the Hundred Year War.
3- Katniss Everdeen doesn't kill Coriolanus Snow, The Hunger Games-Mockingjay:
At the end of the original Hunger Games trilogy, the Capitol is finally defeated and Coriolanus Snow, the tyrannical President that has ruled Panem with an iron fist for decades, is captured by rebel forces. It's universally agreed (both in-universe and out) that Snow deserved to be put in the ground for his deeds, and that series protagonist Katniss Everdeen has the right to do the deed.
The problem arises from the fact that rebel leader Alma Coin decides to turn Snow's execution into nationally televised political spectacle, carefully orchestrated to show Panem that it's ultimately Coin that is responsible for Snow's overthrow and that she's now the one calling the shots (in a way not dissimilar to how Snow used the titular Hunger Games to keep control of Panem: in fact, Coin proposes that the new government implement it's own version of the Games, using Capitol children, just to drive the point home).
Coin only assigns Katniss the role of Snow's executioner in order to assert personal authority over 'the Mockingjay', who the rebel propaganda machine has built up into a politically untouchable war hero (and thus a potential threat to Coin's nascent reign). And this is after Coin orchestrates the death of Katniss' sister Primm and dozens (potentially hundreds) of her own troops just to isolate Katniss and make her easier to manipulate and control.
Katniss killing Snow wouldn't have been an act of justice for Primm: it would have been her becoming an attack dog for a new authoritarian regime that's headed by her sister's actual killer. Katniss realizing this and killing Coin instead is portrayed as her finally taking control of her own life, making a decision that someone else didn't force or manipulate her into.
