In the fanfiction, they could leave in search of a way to strengthen their abilities. Konoha might not have the resources or the right training for them at that point. They might believe that by leaving and traveling, they can find new mentors or training methods that will make them stronger.
Perhaps they leave because of some danger that threatens them specifically in Konoha. For example, there could be a group within the village that doesn't like their relationship or has some vendetta against them. So, they decide to leave to protect themselves and their future family.
One reason could be to find a more peaceful place. Maybe after all the chaos in Konoha, they just want a quiet life away from it all. They might also leave to explore the world and discover new things together, like new jutsus or different cultures.
They might leave to seek new forms of power or knowledge. There could be things outside of Konoha that they believe will help them become better at their ninja skills. For instance, they might have heard of a special dojo or a hidden scroll in another land that could enhance their abilities.
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 a sense of disillusionment. Maybe Naruto discovers some dark secrets within Konoha's leadership that make him question his loyalty. For example, if he finds out that some decisions were made that put the village at risk for the wrong reasons.
One possible reason could be a mission gone wrong. Maybe they are framed for something during a mission outside Konoha and feel they can't return until they clear their names. For example, if they are accused of stealing a valuable artifact from a village they were helping, they might choose to leave Konoha to find the real culprit and prove their innocence.
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.
One possible reason could be to seek a new life away from the politics and pressures of Konoha. Maybe they feel restricted by the village's rules and expectations. Another reason might be for a personal adventure. They could be in search of something that Konoha can't offer, like a new type of ninja training or a mysterious power source. Also, it could be related to protecting their family. If they sense some kind of threat to their family within Konoha, they might choose to leave to keep them safe.
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.
It could be due to a threat to their lives within the village. There might be a hidden group in Konoha that has a vendetta against them. Naruto and Tenten, not wanting to put their friends and family in danger, choose to leave. They might plan to return once they have found a way to neutralize the threat.
One possible reason could be that Naruto discovers some dark secrets about Konoha that shatter his idealized view of the village. Maybe he finds out that the village elders were involved in unethical practices, like using shinobi for immoral experiments. This would make him lose faith in Konoha and decide to leave.
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.