She could be an original character created specifically for this fanfiction. The author might give her unique abilities and a distinct personality to make the story more interesting.
Perhaps in this fanfiction, his sister has done something wrong or dangerous, and Naruto has to 'beat' her in the sense of stopping her. It could involve a moral or ethical conflict within the story that Naruto has to resolve by overpowering his sister's actions.
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.
Well, in a way it depends on the context of the fanfiction. If the writer decides to give Naruto some sort of super - powered boost or if Jiraiya is weakened in some way. For example, if Naruto has some unique power - up that allows him to counter Jiraiya's toad - related jutsus easily. But Jiraiya is a very experienced and powerful shinobi too, so it's not a straightforward win for Naruto without some plot devices.
One possible reason could be to protect her. Naruto might believe that by leaving, he can draw danger away from his sister. For example, if there are powerful enemies targeting him, he doesn't want his sister to get caught in the crossfire.
The relationship could start with Naruto being overly protective of his sister, but she wants more independence. This causes friction. Later, when she gets into trouble that only Naruto can help her with, he steps in. This makes her realize that his over - protectiveness comes from love, and they begin to repair their relationship. For instance, if she is kidnapped by a powerful enemy, Naruto uses all his skills to rescue her, and during this process, they have heart - to - heart conversations.
One idea could be that their own village betrays them. Maybe there's a power - hungry leader who sees Naruto and his sister as threats to their new regime. They could be framed for a crime they didn't commit and then forced to flee the village. In the process, they might have to rely on some unlikely allies they meet on their journey, like a group of outcasts who also have a grudge against the village.
She could be very sad. After all, Naruto is likely an important person in her life. She might feel abandoned and start to question why Naruto left her.
Maybe she's jealous of Naruto's popularity or his strength. It's possible that she feels overshadowed by him all the time and that jealousy turns into resentment, leading her to hurt Naruto.
Communication is key. Naruto and his sister could sit down and have an honest conversation about what's bothering him. They could clear up any misunderstandings that led to his hatred.