It could also be due to a power struggle. Naruto is extremely powerful and independent. If Rias or other members of the peerage try to control or limit his power in some way, he would not tolerate it. His power is a part of who he is, and he's used to using it freely to protect others. So this could lead to his departure from the peerage.
One possible reason could be a difference in their goals. Naruto is from the Hidden Leaf Village with a mission to protect it and promote peace there. Rias, on the other hand, has her own responsibilities in the Underworld. Their conflicting duties might lead to Naruto leaving.
It might be a simple matter of territoriality in the fanfiction. Naruto has his own group of friends and comrades in his own universe. When he encounters Rias Peerage, he could feel threatened by their presence or the way they interact with the characters in his world. Also, the power structures are different. Naruto's power comes from his own training and the chakra within him, while the Peerage gets power from different sources like contracts and devil heritage. This disparity could lead to dislike.
One possible reason could be a desire for self - discovery. Issei might feel that being in Rias' peerage limits his growth in certain ways. He may want to explore his powers and identity on his own terms.
One possible reason could be Naruto's independent nature. He has always been someone who forges his own path. In the Naruto series, he doesn't rely on traditional forms of status or hierarchy. So in the fanfiction, he might refuse peerage because he wants to be recognized for his own efforts and not because of a title.
In this fanfiction scenario, Naruto's unique abilities like his shadow clones and rasengan would be interesting to see in the context of being kidnapped by Rias Peerage. Maybe the Peerage kidnapped him because they saw his power and wanted to use it for their own purposes. Naruto might resist and start training in secret to get stronger and break free. He could also form an alliance with other characters who oppose Rias Peerage in their world.
In a Naruto - Rias' peerage fanfiction, the story might focus on how Naruto's chakra system interacts with the devil's power. For example, his ability to sense chakra could be enhanced or changed when combined with devilish senses. Also, his relationship with the members of the peerage would be interesting. He could form strong bonds with some, like Kiba in Naruto's world, he might get along well with the werewolf in Rias' peerage.
Another possible reason is that Naruto might be protective of his own story's integrity. He has been through a lot in his own series, and the Rias fanfiction might seem like an intrusion or a misappropriation of the idea of fictional characters. It's like his world and story are his own, and the fanfiction is trying to merge it with something else in a way that he doesn't like. He may feel that his own story should be kept separate from this other fan - created content.
One possible plotline could be that Naruto has his own mission or purpose that is in conflict with Rias's plans or the world she is a part of. So, he decides to leave to pursue his own goals. For example, he might need to go back to the Hidden Leaf to protect it from a new threat that only he can handle. Another could be that Naruto discovers some dark secret about Rias or her group and can't stay with them any longer. He values his own moral code too much to be associated with something he deems wrong.
One reason could be the motherly love. Kushina always loved Naruto deep down. Leaving him means missing out on his growth and important moments in his life. Another reason might be realizing the hardships Naruto faced without her presence. She probably feels guilty for not being there to protect him from the loneliness and the many challenges he had to endure in the village.
One possible reason could be that Naruto has a dangerous mission that only he can undertake. The safety of the village or the greater good might demand his immediate departure, even though it's hard for him to leave Hinata in such a state.