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.
I'm not aware of any official 'Naruto kills his sister' fanfiction. This goes against the general nature of Naruto's character who values family and friends. Fanfiction that involves such extreme and out - of - character scenarios might be very rare or non - existent in the mainstream Naruto fanfic community.
It could be an original character created just for the fanfiction. Many fanfiction writers like to introduce new characters to add their own unique twists to the story.
At first, Sasuke might not believe it was Naruto's own will. He would try to find out if Naruto was under some sort of external influence. But if he found out that Naruto was fully responsible, Sasuke's reaction would be one of pure hatred. He would abandon all his previous beliefs and goals and make it his sole mission to destroy Naruto. He might also cut off all ties with the village that Naruto was protecting, seeing it as an accomplice in his sister's death.
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 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.
This is a really dark concept. In fanfiction, such a scenario might be written to explore extreme emotional distress. Maybe the author wants to show how much pressure Naruto has endured secretly, and on his birthday, which is supposed to be a happy day, it all becomes too much to bear. However, in the original Naruto story, Naruto is a character full of hope and perseverance, so this is a very different take.
In the Naruto series, Naruto doesn't have a biological sister in the original story. So in this fanfiction, the author probably creates a new character to be his sister. It could be an original character with unique abilities and a complex backstory that leads to the situation where Naruto dies by her hand.
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.
One possible plotline could be that Naruto is under some sort of dark magic or mind control. Maybe an enemy has found a way to manipulate his actions and make him turn on his friends. Another could be a situation where Naruto is tricked into believing his friends are actually enemies in disguise. For example, if there was a powerful genjutsu that made him see his friends as threats to the village.