One possible reason could be that his sister has some special or unknown powers that Naruto doesn't understand. For example, if she has a very unpredictable and potentially dangerous kekkei genkai. Another reason might be that she has a very strong and intimidating personality, which makes Naruto feel small and scared in her presence.
It might show Naruto's vulnerability. Usually, Naruto is seen as a brave and determined character. But being scared of his sister reveals that he has his own insecurities. This can add depth to his character as it shows he's not just a fearless hero all the time.
Naruto would use his ninja skills. He might start with a diversion, like creating some clones to distract the assassin while he gets his sister to a safer place.
I'm not sure if there is such a specific fanfic. Fanfics cover a wide range of themes, but abuse within family in a Naruto fanfic might be a rather dark and not - so - common take. It could exist in some corners of the vast fanfic community, but it would also be quite controversial as Naruto is generally depicted in positive relationships in the original series.
It could be due to a misunderstanding. Perhaps there was an incident where his sister was involved, but Naruto misinterpreted her actions as something malicious against him. Like she might have accidentally broken something precious of his and he thought it was on purpose.
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.
One common theme is self - discovery. Naruto's jealousy makes him look inward and realize his own insecurities. Another theme is family dynamics. It shows how jealousy can strain or strengthen the relationship between siblings and within the family. For example, Naruto might initially resent his sister but later learn to support her.
In this fanfic scenario, Naruto's character could take a darker turn. Maybe he becomes more solitary and distrustful. His sister, on the other hand, might be favored by Kushina but have her own internal struggles. The story could explore how Naruto overcomes his feelings of being abandoned and reconciles with his family.
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.