One possible reason could be for Naruto's protection. Maybe she thought by banishing him from a certain place or situation, she could keep him away from a hidden danger that she knew about. For example, there might be a powerful enemy targeting Naruto specifically, and she believed that by making him leave, he would be harder to find.
Another aspect could be that the fanfiction delves into how Kushina's presence affects Naruto's relationships with others. For instance, his relationship with Sasuke could be different. With a strong maternal figure in his life, Naruto might be more stable emotionally and be able to approach Sasuke in a more understanding way, which could potentially change the whole dynamic of their rivalry and friendship.
One possible reason could be some sort of dark influence or curse that makes her lose her maternal instincts. Maybe a powerful enemy targets her and in order to protect Naruto from further danger related to her, she feels forced to abandon him. Another reason might be that she is made to believe false information about Naruto, such as that he will bring great disaster to the village in the future.
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.
He could learn powerful sealing techniques. Kushina was known for her sealing skills, and she could pass them on to Naruto. This would give Naruto an advantage in battles and also in containing the Nine - Tails' power.
They would likely develop a complex relationship. On one hand, Kushina is his sensei, so there would be a sense of respect and authority. But on the other hand, Naruto knows she is his mother in the original story, so there might be an underlying emotional bond. It could be a relationship where Naruto looks up to Kushina as a mentor but also feels a deep connection that is different from a typical student - teacher relationship.
It could also be due to some external influence. Perhaps an enemy used some kind of mind - control or manipulation on Kushina. They made her think that Naruto was a threat, so she decided to disown him. In the Naruto universe, there are many powerful villains who could potentially do this kind of thing.
Maybe she's been possessed. In some fanfictions, characters can be taken over by dark forces. So Kushina could be under the control of some evil entity and that's why she hurts Naruto.
Kushina Uzumaki was known for her fiery red hair and strong will. She was a Jinchuriki, just like Naruto, which made her both powerful and a target. Her love for her family, especially Naruto, was unwavering. Even though she sacrificed herself early in Naruto's life, her influence on him was profound.
Kushina was also very kind - hearted. Despite her tough exterior as a ninja, she had a soft side. This was evident in how she cared for Naruto, even though she couldn't be with him as he grew up. She passed on her love and values through her sacrifice.