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.
One possible reason could be that Naruto feels he has learned all he can from Jiraiya at that point. Maybe he wants to explore his own path independently and test his skills without Jiraiya's constant guidance.
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.
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.
It can create a sense of growth for Naruto. Without Jiraiya by his side, he has to rely more on his own instincts and the skills he has already acquired. This can lead to new character development as he faces challenges alone.
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.
A fanfic like this might explore how fem Naruto's presence affects Jiraiya's typical behavior. Jiraiya is known for his pervy tendencies in the original series, but with a fem Naruto, he might have to control himself more. It could also be about how fem Naruto looks up to Jiraiya as a strong ninja and a source of wisdom, and how she tries to learn from him to become a great kunoichi.
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.