One possible plot could be that Dark Naruto leaves Jiraiya because he feels that Jiraiya's teachings are not in line with his new dark path. He might have been influenced by some dark force or his own inner demons. He then goes off to explore his own power, perhaps seeking out other dark entities to team up with, leaving Jiraiya feeling like he has failed as a mentor.
Well, it could be that Dark Naruto is tired of Jiraiya's attempts to control or change him. He has a different vision for himself and his power. Maybe he wants to use his dark abilities to take over a certain territory or gain a particular item. Since Jiraiya is constantly trying to stop him from using his dark side, he decides to leave Jiraiya behind and pursue his own goals, regardless of the consequences.
Perhaps in the fanfic, Dark Naruto realizes that his presence is causing unrest in the village after the Chunin Exams. He doesn't want to be a source of trouble for those he cares about, like his friends or even his sensei. So he chooses to leave to protect them. He might embark on a journey to learn more about his dark side and how to control it away from the village.
It can create a sense of growth for Naruto. Without Jiraiya by his side, he has to rely more on his own instincts and the skills he has already acquired. This can lead to new character development as he faces challenges alone.
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 plot could be that Naruto, having achieved a god - like state of power, feels he has outgrown Jiraiya's teachings. He might leave to explore new realms of power on his own. He could be on a quest to face threats that Jiraiya no longer has the ability to help him with, and he wants to protect the village in a way that goes beyond what Jiraiya has shown him.
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.
Perhaps they leave because they discover a new threat that the ninja villages are not taking seriously. Naruto and Sasuke decide to take matters into their own hands. They travel to different places, gathering information and allies. Their relationship also evolves during this time, from just comrades to true brothers who understand each other completely.
At first, Jiraiya would be in shock. He couldn't believe that Naruto has become so dark and left him. Then, he would be determined to bring Naruto back. He would follow Naruto's trail, trying to understand his motives. Along the way, he might face some challenges from Dark Naruto's new allies or the places he visits. But Jiraiya would not give up easily, as he truly cares about Naruto and wants to save him from the darkness.
One possible plot could be that Naruto goes on a special training journey with Jiraiya again, but this time they encounter a new and powerful enemy that has a connection to Jiraiya's past. Naruto has to learn a new jutsu from Jiraiya to defeat this foe.
One possible plot could be that Naruto has been misinformed about Jiraiya's actions. Maybe he heard false rumors that Jiraiya was involved in something bad. So, he decides to ignore Jiraiya out of disappointment. As a result, Jiraiya has to find ways to prove his innocence and regain Naruto's trust.
One possibility is that Naruto comes back much stronger and more confident. He might show off some new jutsu to his friends like a more powerful Rasengan. His return could also stir up the village as they see his growth and start to have new hopes for the future.