One reason could be the close bond they had in the original story. Jiraiya was like a father figure to Naruto in some ways. So in fanfic, it's a natural extension to make him Naruto's actual dad. Another reason might be to create new plot twists. For example, it could lead to different power inheritances or story arcs related to Naruto's family history.
In many Naruto fanfics, there are all kinds of creative interpretations. Some might make Jiraiya Naruto's dad in their fictional stories. However, in the original Naruto series, Naruto's father is Minato Namikaze. But fanfics give authors the freedom to rewrite relationships in unique ways.
One possibility in a fanfiction where Jiraiya is alive could be that he returns during the Fourth Great Ninja War. He could use his vast knowledge and powerful jutsu to turn the tide of the war. Maybe he teams up with Naruto again and helps him master new forms of the Rasengan or other powerful techniques.
One possible fanfic could involve Naruto learning unique jutsu from Jiraiya due to his Rinnegan. Maybe Jiraiya, with his vast knowledge, would train Naruto in ways that are different from the original story. For example, Naruto could master space - time ninjutsu related to the Rinnegan earlier, which would give him an edge in battles against stronger opponents like Akatsuki members. He might also use the Rinnegan to understand the secrets of the tailed beasts more deeply, leading to a different relationship with Kurama.
One consequence could be a stronger sense of family heritage for Naruto. He might inherit more than just skills from Jiraiya but also a deeper family legacy.
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.
Well, it's sort of popular. Some fans really like the idea as it gives a new spin on Naruto's story. It can open up possibilities for different plotlines, like how would Jiraiya and Tsunade raise Naruto. But on the other hand, it goes against the original canon, so not all fans are into it.
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.
In the fanfiction, Jiraiya often tells Naruto stories about his past adventures. These stories are not just for entertainment but also to teach Naruto about courage, perseverance, and the values of a ninja. For instance, the stories of Jiraiya's battles with powerful enemies show Naruto what it takes to be a strong and respected ninja. Jiraiya also protects Naruto when they are in dangerous situations, putting Naruto's safety above his own, which is a very fatherly thing to do.
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.