Perhaps they discover a dark secret within Konoha that they can't abide by. It could be something related to the upper echelons of the village making unethical decisions. Like if they find out that the village is secretly using forbidden jutsu on its own people for experimentation, Naruto and Kakashi might leave to expose this truth from the outside.
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 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 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.
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.
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.
Perhaps there was some sort of dark influence or mind - control at play. An enemy might have manipulated Kakashi's mind in such a way that he believed Naruto was a threat and thus left him for dead, not realizing his true self.
One reason could be to protect Konoha from a great danger that he can only face by leaving. Maybe there's a powerful enemy who has a vendetta against Naruto but would spare Konoha if he goes far away. Another reason might be a sense of self - exile due to some event that made him feel he no longer belongs in Konoha, like a misunderstanding where the villagers turn against him again.
Perhaps he is lured away by an unknown force. In some fanfictions, there might be a mysterious character or group that tricks Naruto into leaving Konoha. They could make false promises about his parents or his true power, making him curious enough to follow them.
One possible reason could be for his safety. Konoha is a well - protected village with many skilled ninja. She might believe that leaving him there would ensure he has the best chance at survival and growth as a ninja. Also, she may have some mission or obligation that forces her to leave him behind, perhaps something related to the greater good of the village or the ninja world in general.