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 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.
One possible reason could be to avoid the political intrigue in the village. With his new inheritance, he might feel that he can't fully develop or use it while being constantly under the watchful eyes and political games in the village.
One possible reason could be to seek greater power and training opportunities elsewhere. Maybe he feels restricted within his clan in terms of the type of jutsu he can learn or the level of training he can receive. So, he decides to leave to explore different ninja arts and grow stronger on his own terms.
One possible reason could be to protect her. Naruto might believe that by leaving, he can draw danger away from his sister. For example, if there are powerful enemies targeting him, he doesn't want his sister to get caught in the crossfire.
One possible reason could be that Naruto might feel Jiraiya is being too overbearing in his training methods. In some fanfictions, Jiraiya might push Naruto too hard without considering his emotional state, leading to Naruto snapping.
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 reason could be a mission. Maybe he gets a top - secret mission that requires him to leave the village under Tsunade's leadership without her direct involvement. So he has to leave without much notice.
One possible reason could be a sense of disillusionment with the village. Maybe he feels unappreciated for all his efforts in protecting Konoha. Another reason might be that he is being framed for something bad in the village and decides to leave rather than face false accusations. Also, he could be lured by the promise of a greater adventure outside Konoha that is not directly related to money.
One possible reason could be that the writer lost inspiration. Jiraiya has a complex character in the Naruto series, and it might be difficult to keep coming up with new and interesting plotlines for him in fanfiction. Another reason could be that the writer got involved in other projects or fandoms and simply didn't have the time to continue with the Naruto fanfiction centered around Jiraiya.
One possible reason could be jealousy. Maybe in the fanfiction, Jiraiya gives more attention to another character, and Naruto, being young and impulsive, starts to hate him for it.