One reason could be to explore a different side of Harry's character. In the original books, he's very much a social character in some ways, but by having him keep to himself, the author can show his more introverted and introspective side.
In such a fanfiction, Naruto keeping to himself might make others initially find it hard to approach him. For example, his friends like Sasuke and Sakura might be a bit confused at first. Sasuke, who is also a bit of a loner in his own way, might not know how to deal with this new Naruto. Sakura, on the other hand, might try harder to break through his shell. This could lead to some strained relationships at the start, but as the story progresses, those who truly care about Naruto would try to understand him better and build deeper, more meaningful relationships with him.
One popular 'Harry keeps to himself' fanfiction could be 'The Silent Gryffindor'. In this story, Harry's decision to keep to himself is due to the overwhelming attention he gets after the events with Voldemort. He withdraws into himself to find some peace and self - discovery.
One possible reason could be the burden of his past. Naruto has faced a lot of hardships and the memories might be overwhelming him, making him want to be alone. For example, the loss of his master Jiraiya might have left a deep scar, and he might feel that isolating himself is the only way to deal with that pain.
Maybe he feels a sense of guilt. For example, if something bad happened in the village that he blames himself for, even if it wasn't really his fault. He could exile himself as a form of self - punishment. He has always been very hard on himself when it comes to the well - being of the village and his friends.
Jiraiya is another person. Since Jiraiya trained Naruto and was like a father figure to him. Naruto could write about their travels together, the lessons Jiraiya taught him, and how much he misses Jiraiya after his death. He might also mention the pervy things Jiraiya did that always made him laugh.
Well, while there might be some out - of - character fanfictions out there, the general perception of Naruto is that he is a very selfless character. His whole journey in the original story is about protecting others and achieving peace for everyone. So, in fanfiction, it's not very common for him to be portrayed as only caring for himself. Usually, the essence of his character is maintained, which is his altruism.
In some fanfictions, Naruto might distance himself because he discovers some dark secrets about the ninja world or his own past. These revelations could shock him so much that he needs time alone to process and figure out how to deal with them.
Perhaps in the fanfiction, Naruto discovers some dark secrets about his past, like his family's involvement in something he considers immoral. This new knowledge could make him question his own identity and lead to self - hatred. He might feel that he's a product of something bad and that he can't escape this 'taint' no matter how hard he tries.
In fanfiction, Naruto sacrificing himself for Obito could be a very emotional and dramatic concept. It might show Naruto's ultimate selflessness, believing that Obito is worth saving at the cost of his own life. This could be due to Naruto seeing the good in Obito that others might not, like the part of Obito that was once a kind - hearted shinobi.