One factor could be a new and extremely powerful jutsu. For instance, if Naruto creates a jutsu that combines the power of the Nine - Tails and Sage Mode in a way that Jiraiya can't defend against. Another could be an unexpected advantage like having insider knowledge about Jiraiya's weaknesses. Maybe he learned something from Tsunade that gives him an upper hand.
In fanfiction, Naruto could beat Jiraiya if he has some sort of emotional advantage. For example, if the story is set in a situation where Naruto is fighting to protect someone very dear to him, like Hinata or his children in a future - set fanfic. This extra motivation could push him to tap into deeper reserves of power and outperform Jiraiya. Also, if Naruto has made alliances with other powerful characters who can assist him during the fight, that could be a game - changer.
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.
Jiraiya may provide Naruto with emotional support in fanfiction. Since Naruto grew up without his parents, Jiraiya becomes like a father figure. He encourages Naruto when he's down and helps him understand his own strength. For example, he might share stories of his own past failures and how he overcame them, which gives Naruto the motivation to keep going.
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.
In this fanfiction, perhaps Jiraiya didn't actually die. He was in a hidden place recovering from a serious injury. When he meets Naruto again, Naruto is shocked but overjoyed. Jiraiya then shares his newfound knowledge and powers with Naruto, and they team up to take on a powerful organization that threatens the Hidden Leaf Village. Jiraiya could teach Naruto some advanced Sage Mode techniques that he had been working on during his absence.
The plot might involve Naruto and Jiraiya getting transported to a different dimension. In this strange new world, they have to work together to find a way back home. They meet all kinds of strange creatures and characters. Jiraiya uses his wisdom and experience to navigate through this new environment, while Naruto's determination and growing power help them face the challenges. And during this adventure, Naruto might also develop a new form of his Rasengan, inspired by the things they encounter in this dimension.
One reason could be that Naruto might feel he has outgrown Jiraiya's teachings in the fanfiction. He may want to explore his own path independently. Another possibility is that Naruto gets involved in a mission or a situation where he has to part ways with Jiraiya for the greater good. For example, if there is a threat in a far - off land that only Naruto can handle, and Jiraiya has other commitments elsewhere.
One possible plot could be that Jiraiya is forced to betray Naruto due to some external threat. Maybe an enemy has captured Jiraiya's loved ones and threatened to kill them if he doesn't turn on Naruto. Jiraiya, in a difficult position, might have to pretend to be against Naruto to protect his loved ones while secretly trying to find a way to free both Naruto and his family from the enemy's clutches.
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.
Well, one possibility is that Naruto would grow up with more focused and intense training. Jiraiya could pass on his unique jutsu more directly. Maybe Naruto would learn about the world outside of Konoha in a more in - depth way earlier on, traveling with Jiraiya and having adventures that shape his understanding of the ninja world and his place in it.