One possible scenario in this fanfiction could be Jiraiya taking on the role of a mentor to young Naruto even more intensively. He might teach Naruto some unique jutsu that are not part of the original storyline. For example, he could introduce Naruto to some ancient toad - related techniques that are only known within the toad clan.
In this fanfiction, Jiraiya might also take Naruto on some adventures. They could go on a journey to explore some hidden places in the Naruto world. Along the way, Naruto would learn not only about combat skills but also about different cultures and histories within the world, which would shape his character in new and interesting ways.
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.
Jiraiya's reaction might be complex. He might be in awe of Naruto's new power but also sad about his departure. He could see it as a natural progression in Naruto's journey, yet still feel a pang of loneliness. He might start to reflect on his own life and training methods, wondering if he could have done something differently to keep Naruto with him. At the same time, he would be eager to see what Naruto will achieve in the world with his newfound abilities.
They often make him seem irresponsible. For example, in normal Naruto story, Jiraiya is seen as a mentor to Naruto. But in bashing fanfiction, he may be shown as being more interested in his own adventures and leaving Naruto alone at crucial times.
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.
Jiraiya is frequently shown as a very dedicated mentor. He is willing to sacrifice his own time and resources to train and guide his students. In some fanfictions, he goes to great lengths to protect his students from harm, even putting his own life on the line. This selfless aspect of his character is often emphasized.
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.