Disclaimer: Avatar the Last Airbender copyright Dante Dimartino, Brian Konietzko and Nickelodeon Studios.
Kill the flesh while Koh squats within. Kill Zuko to save the world. For the first time, Katara had an inkling of the impossible choice Aang had been given. While former Fire Lord Ozai deserved capital punishment, killing him would've gone against every moral belief Aang held; even if it was for the good of the world. In Aang's eyes, everyone was redeemable.
The Water Tribe held different views on an enemy's death. She wouldn't have hesitated in killing Ozai, but Zuko was not an enemy even if the creature currently inhabiting his body was. How could she kill him?