It could also be due to some sort of prophecy or family secret. Maybe his father believes that Naruto needs to be isolated until a certain time or event occurs. For example, if there is a prophecy that Naruto's power will become uncontrollable at a young age, his father might lock him away to prevent any disasters.
Another reason could be related to political unrest. If Naruto's father is in a difficult political situation, he may fear that Naruto could be used as a pawn. So, to prevent this, he locks Naruto away to keep him out of the political games that are being played in the ninja world.
One possible reason could be for Naruto's protection. His father might think that by locking him away, he can keep Naruto safe from the many threats in the Naruto world, like powerful enemies who might target Naruto for his special powers.
One reason could be that some in the village feared his potential as the Jinchuriki of the Nine - Tails. They might have thought locking him away would prevent him from causing chaos. Another reason could be related to those who still held grudges against the Fourth Hokage for sealing the Nine - Tails in Naruto. They took it out on Naruto by imprisoning him.
Another reason could be for disguise. Naruto might be in a situation where he needs to hide his identity. By covering his eyes, which are a very recognizable feature of his, he can make it more difficult for others to figure out who he is. This could be especially important if he is in enemy territory or trying to infiltrate a group secretly.
One possible reason could be that Naruto feels abandoned. His father was not around during his childhood, and he had to face a lot of hardships alone. Growing up without a father figure, he might have developed resentment.
One possible reason could be a sign of extreme loyalty and friendship. Naruto might see Yang in a dire situation where she needs his arm for some crucial purpose, like to complete a powerful jutsu or to defend against an overwhelming enemy. He is known for his selfless nature, so sacrificing his arm would be in line with his character.
Well, in this fanfiction, it could be that Naruto is locked away by a powerful enemy of the village who wants to use him as a weapon later. Maybe Orochimaru gets his hands on Naruto as a baby and locks him in one of his secret labs. There, Naruto endures all kinds of experiments and hardships. But through his natural tenacity, he starts to develop unique abilities that are a combination of his jinchuriki powers and Orochimaru's experiments. Eventually, he escapes and has to decide whether to use his new powers for good or for revenge against the village that failed to protect him.
At first, Naruto might be confused and hurt. He doesn't understand why his father would do such a thing to him. He may feel betrayed since he expects his father to be a source of love and protection, not confinement.
Maybe he's being punished for some misdeed in the fanfiction world. For example, if he accidentally broke an important village rule or caused some chaos during a mission. Another reason could be that someone is trying to keep him safe from an outside threat. They might think that locking him in his house is the best way to protect him from enemies who are after him.
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.
It could be that Naruto discovers some secrets within his family that make him feel uncomfortable or out of place. For example, if there are hidden agendas or dark pasts that he doesn't want to be associated with, he might choose to move away to start anew.
One reason could be to explore the darker side of the Naruto universe. Writers might want to see how the characters and the world would react to such a major loss.