In the fanfiction, Naruto could leave Hozuki Castle because he feels out of place there. Despite his friendly nature, the culture or the people in the castle might be too different from what he's used to. He might long for the familiar environment of Konoha or his friends, and this homesickness drives him to leave, even if there were unfinished tasks at the castle. His departure could then lead to a journey of self - discovery as he tries to figure out where he truly belongs in the ninja world.
In the 'Naruto leaves after Hozuki Castle' fanfiction, he could be leaving because he's completed a mission there. He might be leaving behind some sort of mystery or unfinished business. Perhaps there was a powerful item or secret at Hozuki Castle that Naruto either uncovered or was unable to fully understand, and his leaving is to seek more knowledge or help regarding it.
One possible reason could be a mission. Maybe the Hidden Cloud Village (Kumo) requests Naruto's help specifically for a very important and dangerous mission that can only be accomplished by him. So, he has to leave Konoha for Kumo.
One reason could be that he feels ostracized. Despite his efforts to protect Konoha, some villagers still look at him with suspicion because of the Nine - Tails inside him. He might just get tired of constantly having to prove himself and decide to leave in search of a place where he can be accepted for who he is.
One common theme is mystery. The Hozuki Castle is often depicted as a place full of secrets waiting to be uncovered. Another theme is power. There might be powerful jutsus or artifacts hidden within the castle that the characters seek.
One possible reason could be to seek stronger opponents outside of Konoha. Naruto might feel that he has outgrown the training opportunities in the village and wants to face greater challenges.
He might face some really tough opponents. In the Naruto world, Hozuki Castle is known for being a dangerous place. Naruto would probably use his signature jutsu like Rasengan to defend himself. Maybe he'd also try to make allies among the inmates there.
Maybe Naruto realizes that his feelings for Sakura are not as strong as he once thought. In the fanfiction, he could have met someone else or had an epiphany about his own emotions. He might leave Sakura to find his true self and explore different relationships.
Sasuke might become more withdrawn. He was always in a sort of rivalry with Naruto, and without Naruto there, he could lose some of his motivation to get stronger. Sakura would be devastated. She cared about Naruto, and his leaving would make her question what went wrong. Kakashi would also feel a sense of failure as a teacher.
It could also be that Naruto is forced to leave Sakura due to some external threat or danger. For instance, if there is an enemy targeting Naruto and he fears that being around Sakura will put her in harm's way, he would choose to leave to keep her safe. This is in line with Naruto's selfless nature as seen throughout the series.
Well, there's 'The Enigma of Hozuki Castle in Naruto'. This fanfiction is quite unique as it combines elements of mystery and action. The story revolves around a group of ninjas trying to solve the mystery of a strange energy source located deep within Hozuki Castle. They encounter many foes and obstacles along the way, making it a very exciting read.