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.
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.
One popular Jiraiya fanfic could be those that explore his early days as a ninja. They might focus on his training with Hiruzen Sarutobi and how he developed his unique skills.
Well, 'anti jiraiya fanfic' could be about portraying Jiraiya in a negative light. It might focus on his flaws, like his womanizing ways which some might see as a negative trait. It could also explore scenarios where his actions have unintended bad consequences, rather than the heroic image he usually has in the main Naruto storyline.
I'm not entirely sure as I haven't read it specifically. But it might be about the adventures of Jiraiya, who is often considered a hero in some fictional universes. He could be on a journey to save his world, or perhaps facing some great challenges against powerful enemies.
Another reason could be that Jiraiya has some doubts about Naruto's readiness or potential. He might think that Naruto is not yet at the level where he can fully benefit from Jiraiya's training. For example, Naruto may lack some basic skills or knowledge that Jiraiya believes are necessary prerequisites for his more advanced training.
One unique method could be training in extreme environments. Jiraiya might take Naruto to a desolate desert or a freezing tundra to test his endurance and ability to adapt. This forces Naruto to find new ways to use his chakra and skills.
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.