Perhaps in the fanfiction, Naruto discovers that Sasuke has a new goal that completely opposes Naruto's values. For example, Sasuke might be planning something that would endanger the entire ninja world in a way that Naruto can't accept. Naruto, being the hero he is, has to think about the greater good. He realizes that he can't change Sasuke's mind and thus gives up on him, although it's a very difficult decision for Naruto as Sasuke was once his closest friend.
One possible reason could be that Naruto realizes Sasuke is too far gone on his dark path. After numerous attempts to bring him back, Naruto might start to think that Sasuke doesn't want to be saved. He may see that Sasuke's actions are causing too much harm to the village and the people he loves, and Naruto has to prioritize them over Sasuke. So, he gives up on the idea of bringing Sasuke back.
One possible reason could be the overwhelming loss he has faced. He's lost many dear friends and mentors throughout his journey. For example, when Jiraiya died, it was a huge blow to him. Another reason might be the constant pressure of being the savior of the village. The weight of everyone's expectations could lead him to feel so tired and defeated that he gives up on life.
One possible reason could be that Naruto realizes Sasuke is too far gone in his quest for revenge. Naruto might see that no matter how much he tries, Sasuke won't change his ways, so he gives up. For example, if Sasuke keeps attacking innocent people in his pursuit of power to defeat Itachi's enemies, Naruto might finally lose hope.
Maybe Naruto gets tired of always chasing after Sasuke. He has his own life and dreams too. He might think that he has sacrificed enough of his time and energy on Sasuke, and it's time to focus on himself and the village. He could start to believe that Sasuke has made his own choices and he can't keep forcing Sasuke to come back.
Another reason might be related to Naruto's growth in the fanfiction. If Naruto becomes too powerful or changes in a way that Hinata no longer feels connected to him, she could give up. Suppose Naruto starts to embrace a more solitary and power - hungry path, which goes against Hinata's values of family and connection. This divergence in their paths could cause her to lose hope in their relationship and give up on him.
In some fanfiction, Naruto could give up on Sasuke if he falls in love and his new relationship makes him see things differently. His new partner might convince him that Sasuke is a lost cause or that he should focus on their own future instead. Also, if Naruto suffers a major setback in his own life, like losing a dear friend in a fight related to Sasuke, he could lose the will to keep chasing Sasuke. This would be a very emotional and complex turn of events in the fanfiction world.
Well, perhaps it's because of Sasuke's aloof nature. Naruto is a very open and friendly person, and constantly feeling shut out by Sasuke could lead to a break - up in the fanfiction. Also, Sasuke's thirst for power might be too much for Naruto to handle. Naruto believes in the power of friendship and hard work, but Sasuke seems to be constantly on a solo mission for more strength, which could create a rift between them.
One possible reason could be pure creativity and the desire to break boundaries. Writers might want to explore a completely different side of Naruto that is not shown in the original series. It could also be a way to shock the readers and get their attention.
Another reason might be related to their different ideologies within the ANBU. Naruto may have believed in a more collaborative and friendly approach within the organization, while Sasuke might have been more focused on individual achievement and power. This fundamental difference could lead to Naruto hating Sasuke in the fanfiction.
One possible reason could be to protect Hinata. Maybe Sasuke has unknowingly made a move or decision that Naruto perceives as a threat to Hinata, so he scares Sasuke to make him back off.
One possible reason could be differences in their future goals. Naruto is highly focused on being Hokage and protecting the village, while Hinata might want a more peaceful, family - centered life. Maybe Naruto's hectic schedule and constant danger make Hinata feel neglected, leading to their break - up.