One reason could be the constant setbacks he faces. He might feel that no matter how hard he tries, he can't achieve his goal. For example, if he fails too many times in battles against strong opponents, he could lose hope. Another reason might be the loss of important people in his life. If someone like Iruka or Kakashi, who have been his pillars of support, were to die, it could shatter his dreams as they are so closely tied to his will to succeed for their sake.
If Naruto gives up on his dream in a fanfiction, the whole Naruto universe would be drastically different. His friends would be shocked. For example, Sasuke might not have the same motivation to grow stronger as Naruto's unwavering determination was always a driving force for him. The village of Konoha would also lose a great source of inspiration. Naruto was always the one to believe in the village's future and strive for its betterment. Without his dream, the hope he spread might fade away, leading to a more gloomy atmosphere in the village.
If Naruto gives up his dream, Sasuke might view him as a weakling. Sasuke has always been competitive with Naruto, and Naruto's giving up could make Sasuke lose respect for him. Their relationship could become strained as Sasuke may distance himself from Naruto, thinking he is no longer the worthy rival he once was.
One possible reason could be a series of misunderstandings. Maybe his family made decisions that he felt were against his principles or dreams, and after repeated attempts to reconcile the differences, he just lost hope. For example, if his family was against his ninja way, which is such a core part of his identity.
The story could take a dark turn. Without his heart, Naruto might become a soulless being, and his friends would be devastated. They might try to find a way to get his heart back. Maybe they search for a powerful sage or some ancient magic that could reverse what has been done.
Another reason might be the loss of important people. If someone like Iruka or Kakashi, who were his pillars of support, were to die in a way that made Naruto feel it was all in vain, he could give up. He might think that without them, his dream doesn't matter anymore.
With his friends, it might create a sense of shock. His friends who have always supported his dream of being Hokage would be surprised. Some might be disappointed, like Sakura who has seen Naruto's growth towards that goal. But others, like Shikamaru, might understand his decision and still support him in whatever he chooses to do. With his family, if he has a family at this point, it could bring a sense of relief as they may not want him to be in such a dangerous and stressful position.
If Naruto gives up on his friends in a fanfic, it would be a huge departure from his character. Naruto is known for his unwavering loyalty. His friends are his strength. Without them, he might become a much darker and more isolated character. He could lose his drive to become Hokage as his friends were a big part of that motivation. Also, the village that values friendship and bonds might see him in a different light, and he could face a lot of ostracism.
It could also be that he is tired of the false expectations created by fanfiction. In fanfiction, his character might be portrayed in ways that don't match who he really is. He wants to be true to himself and his ninja way, so he gives up fanfiction.
He would likely become more cynical. Naruto is usually so full of hope and belief in the good of people, but giving up on his family would make him question his own values. He might start to view relationships as more fragile and be less trusting in general.