It could be Orochimaru. Since Orochimaru has a long - standing feud with Jiraiya and is always up to no good. If Naruto ditches Jiraiya, Orochimaru might see this as an opportunity to manipulate Naruto. He could try to convince Naruto that Jiraiya was holding him back and that he can offer Naruto more power, all while having his own evil plans for Naruto.
One possible plot could be that Naruto has a major disagreement with Jiraiya over his training methods. Maybe Naruto feels that Jiraiya is being too hard on him or not focusing on the right aspects of his growth. So, in a fit of anger or determination, he decides to ditch Jiraiya and go off on his own to train in a new way.
Jiraiya might comfort Naruto by sharing his own experiences. He could tell Naruto about the times he faced difficulties and how he overcame them. For example, he might talk about his training with the toads and how he grew stronger through perseverance.
Perhaps in this fanfiction, Jiraiya discovers that Naruto is going to be the cause of a major catastrophe in the future. He might have seen a prophecy or some sort of sign that convinces him Naruto has to die to prevent this. It could also be that Jiraiya has been misled by false information about Naruto, which makes him think that Naruto has become an evil force that needs to be eliminated.
One possible reason could be that Naruto feels he has learned all he can from Jiraiya at that point. Maybe he has reached a level in his training where he believes he needs new experiences and challenges that Jiraiya can no longer provide.
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 great Jiraiya and Naruto fanfiction is 'The Mentor's Legacy'. It delves deep into how Naruto continues to uphold Jiraiya's teachings long after his death. It shows Naruto using the skills and wisdom passed down by Jiraiya in his battles and in his leadership of the village. Another interesting one is 'Jiraiya's Unfinished Business'. In this story, Naruto discovers some of Jiraiya's hidden notes and secrets that he left behind, which leads him on a new adventure to complete what Jiraiya started.
One possible scenario in this fanfiction could be that Naruto grows up with a more balanced upbringing. Tsunade might teach him medical ninjutsu and how to control his emotions better. Jiraiya, on the other hand, would surely train him in powerful combat techniques and in the ways of the sage. Naruto would probably be more mature and well - rounded at an earlier age, with a combination of Tsunade's tough love and Jiraiya's adventurous spirit guiding him.
Maybe Jiraiya found out some dark secret about Naruto's past, like his connection to the Nine - Tails, and decided to keep it from Naruto. When Naruto eventually discovers this, he would be angry at Jiraiya for not trusting him enough to share the truth. This could lead to a rift between them in the fanfiction.
In fanfiction, Jiraiya seeing Naruto as Hokage can be a very emotional moment. It could be a vision Jiraiya has in a story where he's still alive, or perhaps it's a memory in a story set after his death. This often shows Jiraiya's pride in Naruto and his belief in Naruto's potential to lead the village.