I'm not sure if there is an actual 'naruto kills his sister fanfic' specifically. But if there were, it would be a very twisted take on the Naruto universe. Naruto has always been shown to value family, even if he didn't have a traditional family growing up. He found family in his friends and in the village. So this idea of him killing his sister would be a radical departure from his core values.
The idea of a 'naruto kills his sister fanfic' is quite shocking. In the Naruto world, family bonds are important. Naruto's relationship with his father, for example, was revealed to be a complex and important part of his story. He also formed deep bonds with his friends who were like family to him. For him to kill his sister would mean a complete breakdown of the values that the series has built up over time. It's possible that in such a fanfic, there could be some sort of dark magic or mind control involved to make Naruto do such a thing, but it would still be very hard to justify within the context of the Naruto world.
One possible plot could be that Naruto is forced into a situation where he has no choice but to kill Haku in self - defense. Maybe Haku is under some kind of mind control and attacks Naruto relentlessly.
It could start with a rift between them that becomes unbridgeable. Sasuke might side with a group that Naruto is sworn to oppose. Their ideological differences grow to such an extent that they end up in a final battle. Naruto, with a heavy heart, kills Sasuke perhaps because Sasuke refuses to back down and his actions are endangering too many lives. This would be a tragic departure from the original story where their relationship was centered around mutual understanding and redemption.
If such a fanfiction exists, one possible reason could be a mind - control situation. Maybe an enemy uses some powerful genjutsu to make Naruto believe his sister is a threat, causing him to kill her accidentally. Another reason could be a misinformation plot where Naruto is tricked into thinking his sister has committed some unforgivable crime against the village.
One possible motive could be jealousy. Maybe she was jealous of Naruto's growing power and popularity within the village. Another reason might be related to some dark family secret or a curse that forces her to take his life against her will.
Perhaps the story could start with Naruto finding out that his sister is in a secret location held captive by a dark organization. He embarks on a journey full of challenges. Along the way, he has to overcome various traps and face off against strong opponents. His shadow clones could play a crucial role in distracting the enemies while he reaches his sister. Once he does, he uses his chakra to break any bindings and brings her to safety, all while showing his growth as a ninja and a brother.
In a 'Naruto abandoned for his sister' fanfic, perhaps there's a prophecy that only one of them can bring peace to the village. The elders, misinterpreting it, choose the sister and abandon Naruto. Naruto then goes on a journey outside the village, meets new friends and allies, and discovers new powers. Meanwhile, the sister is having her own struggles within the village, like dealing with the pressure of being the 'chosen one' and realizing that Naruto's abandonment might not have been fair.
Most of the fandom would probably be horrified. Naruto is known for his positive values, and killing a family member is completely against that. There would likely be a lot of criticism towards the author of such a fanfic.
One possible plot could be that Naruto is somehow corrupted. Maybe he's been influenced by a powerful dark force or a powerful enemy has tricked him into believing that everyone is a threat to the world he wants to protect. So, he decides to take extreme measures and kill everyone to 'create peace' in his warped sense.
It could be that there is some sort of misinformation spread by an evil organization. They create false evidence that Batman is planning to destroy Naruto's village. Naruto, being the protector of his village, decides to take pre - emptive action. He tracks Batman down and in a fierce battle, kills him. But then as he starts to investigate further, he discovers the truth and has to live with the guilt of killing an innocent (in this case, Batman who was misrepresented).
One possible motive could be a dark or alternate universe take. Maybe in this fanfic's world, there is some sort of dark magic or mind control that forces Naruto to do it against his will.