In a fanfiction, it could be that Jiraiya took on another student who he seemed to favor more than Naruto. Naruto, being competitive and also longing for Jiraiya's exclusive attention, would be angry. He might feel like all his hard work to impress Jiraiya was in vain, and this could create a lot of tension and conflict in the story.
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.
If Jiraiya made a deal with the village elders that put Naruto in a difficult position without his knowledge. For instance, agreeing to send Naruto on a dangerous mission without his consent just to gain some political advantage for the village. Naruto would be angry at being used and not being informed by Jiraiya.
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.
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.
Their relationship would be very strong. Jiraiya would see Naruto as not just a student, but also as a connection to Minato. He would be strict but also very affectionate. Naruto would look up to Jiraiya as a father figure, since he never really had one. They would share many adventures together, with Jiraiya teaching Naruto about life, love, and ninjutsu.
One possible reason could be that in this fanfiction, Jiraiya might be preoccupied with other important matters. Maybe he has a secret mission that demands his full attention and he simply doesn't have the time to train Naruto. Another reason could be that there is some sort of conflict or misunderstanding between them that prevents Jiraiya from taking Naruto under his wing. For example, Naruto might have unknowingly offended Jiraiya in some way, or there could be a prophecy or external force that is keeping them apart for the time being.