Jiraiya could teach Naruto the basic sealing techniques like the Five - Element Seal. This seal can be used to disrupt an opponent's chakra flow. He might also teach him more advanced storage seals, where Naruto could store items or even his own chakra for later use. Another possible technique could be the Summoning Seal, which Naruto could use to summon various creatures or objects.
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 some Naruto fanfictions, Jiraiya's death might be different from the original. One common way is that he might have had more backup during his fight with Pain. Maybe some new characters created in the fanfiction came to his aid at the last moment, preventing his death. However, in other fanfictions, his death could be even more tragic, like being betrayed by someone he trusted before facing Pain, which weakened him and led to his ultimate demise at the hands of Pain.
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.
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 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.
Perhaps Jiraiya has some personal issues or inner conflicts. He might be dealing with his own past traumas or demons that prevent him from taking on the role of Naruto's trainer. For example, he could be haunted by the failures in his previous relationships or battles, and he feels unfit to train Naruto until he sorts out his own problems.
One possible reason could be that in the fanfic, Jiraiya might have made a decision that Naruto strongly disagreed with, like leaving him alone at a crucial time for a long mission. This could make Naruto feel abandoned and thus start to hate him.
He might miss out on some crucial training. Jiraiya has a lot of knowledge and skills to pass on, and by running away, Naruto could fall behind in his development as a ninja.