One reason could be to seek more power. In some fanfictions, Naruto might feel that the Leaf doesn't offer enough resources or training for him to reach his full potential. So he decides to leave to find a place where he can grow stronger.
It could also be related to a personal mission. There could be a threat outside the Leaf that only Naruto is aware of or feels responsible for. He might leave the Leaf to deal with this threat alone, not wanting to put the village at risk or believing that the village won't support his actions.
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 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.
One reason could be to gain more power. In many fanfictions, Naruto realizes that the threats he faces are far greater than what he can handle with his current skills in Konoha. So, he decides to leave and train in a more secluded and challenging place to enhance his abilities.
Perhaps Naruto has some unresolved issues from his past that he doesn't want to burden his family with. He may think that leaving is the best way to deal with these issues on his own, without putting his family in the middle of his personal turmoil. He might go off on a solo adventure to find himself and come to terms with his inner demons.
One reason could be to seek new challenges. The elemental countries might have become too familiar, and he wants to explore uncharted regions to test his skills further. Another could be to escape from the fame and expectations in the elemental countries. He might feel suffocated by the constant attention and the high standards set for him.
Maybe it's to protect the village. He could discover a threat that he can only face away from the Leaf Village, to keep the danger from directly reaching his home and loved ones. He leaves as a form of self - sacrifice.
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.
One reason could be a sense of not belonging. In the village, Naruto faced a lot of discrimination because he was a Jinchuriki. As a female Naruto, she might face additional issues like gender discrimination. Maybe she feels that no matter how hard she tries, she will never be fully accepted in Konoha, so she decides to leave.
One possible reason could be that she realizes she truly loves Naruto too much to be apart from him. Maybe she left because of some misunderstanding or external pressure, but then comes to understand that her place is by his side. Another reason might be that she sees how much Naruto has grown and changed, and regrets not being there to support him during that journey. Also, she could have found that life without Naruto is just not as fulfilling as she thought it would be.