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.
Maybe Naruto is forced to leave due to some political reasons within the ninja world. There could be some powerful forces that require him to be away from Konoha and his family for a while. Another reason could be that he has to go and find a cure or an important item for Hinata's or the baby's health, if there are some potential threats.
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.
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 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 possible reason could be a huge misunderstanding. Maybe he thought Hinata did something really bad to his friends, like unknowingly leading the enemy to them. Without knowing the truth, his hot - headed nature made him lash out.
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.
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.
Well, one reason could be that Hinata's extreme love for Naruto gets out of hand. In the original series, she's very shy but deeply in love. In a fanfiction, this love could transform into an obsessive - like stalking behavior if the writer wants to explore a darker side of her character.
One possible reason could be a mission. In many Naruto - related stories, missions often take characters away from their families. Naruto might have received a highly important and dangerous mission that requires him to be away from Kushina for a long time.
It could be due to miscommunication. Suppose there was a misunderstanding between her and Naruto. For example, Naruto might have said something that Hinata misinterpreted as him losing interest in their relationship. This confusion could have led her to seek comfort in another person, which unfortunately led to cheating.
One possible reason could be a misunderstanding. Maybe some false information is spread about Hinata that makes Naruto believe she has done something unforgivable. For example, if there's a plot to frame her for treason against the village. Another reason might be for her own safety. Naruto might think that banishing her would keep her away from a greater danger that is targeting her because of her relation to him.