Perhaps in this fanfiction, there is a prophecy about Naruto. Some people might believe that Naruto will bring great change, either good or bad, to the ninja world. Those who want to prevent the 'bad' change or those who want to accelerate the 'good' change might kidnap him from his parents. They think they can influence Naruto's upbringing and future actions according to their own desires.
The Akatsuki is also a possibility. They are after jinchuriki, and if they knew about Naruto's existence as a baby, they might try to kidnap him early. They could think that by having him from the start, they can better control the Nine - Tailed Fox within him.
Perhaps Naruto's parents were cursed or had some sort of premonition about a great danger coming to Naruto if he stayed with them. They believed that by separating from him, he would have a better chance of survival. Fanfiction writers often explore these kinds of emotional and complex scenarios to give a different perspective on Naruto's origin.
In this fanfiction, it could be that Naruto's parents were under some sort of mind - control. Some evil entity could have taken over their minds and made them feel hatred towards Naruto. Also, it might be related to a family secret or feud. There could be something in the family's past that made them believe Naruto was a stain on their family name, even though Naruto himself was innocent. It could also be a case of false information being spread around the village which made his parents believe lies about him.
It could be that in this fanfiction, there are some external influences like an enemy who has manipulated Naruto's mind. The enemy might have planted false memories or ideas in Naruto's head, making him believe that his parents are not who he thought they were, leading to his rejection.
One possible reason could be a sense of betrayal. Maybe he discovers some long - hidden secrets about his family that make him feel they are not who he thought they were. For example, if he found out his parents had some kind of deal with the village elders that he disagreed with.
In some fanfictions, it could be due to his parents being on a dangerous mission. They might have been forced to leave Naruto in order to protect him from the enemies who were after them. Maybe they thought that by abandoning him, the enemies wouldn't be able to find him as easily. Another reason could be that they were under some sort of dark magic or curse that made them act against their will. This could lead to them leaving Naruto without any choice.
One possible reason could be that they are too involved in their own shinobi duties. The world of ninjas is full of dangerous missions, and they might be constantly away on important tasks, leaving Naruto feeling neglected.
One possible reason could be for Naruto's protection. His parents might think that by giving away his birthright, they can keep him away from dangerous enemies or political intrigue in the ninja world. Maybe they foresee a great threat that would target Naruto specifically because of his birthright, and this is their extreme measure to ensure his survival.
A possible storyline is that Naruto starts to suspect that there was a darker reason for his parents leaving him. This could lead to a conflict within himself, whether to forgive them or not. He could also meet other orphans in the village and form a sort of support group. They could work together to change the village's perception of orphans. Another idea is that Naruto discovers a secret about his parents that puts him in danger, and he has to fight to protect that secret while also coming to terms with his feelings of abandonment.
Well, perhaps in the fanfiction world, Naruto's parents discover some kind of 'dark power' within him that they fear might be uncontrollable. They think that banishing him is the only way to keep the village safe from this potential threat. This could be a power that is different from the Nine - Tails' chakra and seems extremely dangerous to them.