In the fanfic, it could be that Naruto has some sort of self - discovery to do. He may have realized that he has been too caught up in the lives of others, including Sakura's. So he decides to leave her alone to explore his own identity and purpose. This departure could be a turning point for Sakura as well, as she might have to re - evaluate her relationship with Naruto and how much she has relied on him.
Maybe Naruto leaves Sakura alone because he has a new mission that requires him to be solo and he doesn't want to put Sakura in danger. He has always been protective of her, but in this case, he believes the best option is to go it alone. This could lead to Sakura having to become more independent and rely on her own skills rather than depending on Naruto.
One possibility is that Naruto realizes Sakura has feelings for Sasuke that he can't change, so he decides to focus on his own ninja journey alone and leaves her to figure out her relationship with Sasuke. He might feel that his presence is only causing confusion or getting in the way of her true feelings.
One reason could be that Naruto realizes his feelings for someone else and doesn't want to mislead Sakura. In some fanfictions, Naruto might discover that his true love is Hinata and so he steps away from Sakura to pursue a relationship with Hinata without causing any confusion for Sakura.
One possible scenario could be in a fanfic where Sakura accidentally uses her strength during a training session with Naruto and physically hurts him. Maybe she misjudges her punch or kick.
In this kind of fanfic, one possible scenario could be that Naruto leaves Konoha due to feeling misunderstood. Maybe he has been wrongly accused of something and decides that he can't stay in a place where people don't trust him.
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.
She might be initially shocked and hurt. Sakura has always had Naruto as a constant in her life, so his sudden absence would be difficult to accept. She could become withdrawn and start to question her self - worth.
Perhaps Sakura is alone as a result of a broken relationship. She finds out she's pregnant and has to make a decision about whether to keep the baby or not. If she decides to keep it, she starts to build a new life for herself and the unborn child. She might learn new skills, make new friends who support her during the pregnancy, and gradually become more confident in her ability to be a single mother.
One possible scenario could be that Naruto leaves due to a misunderstanding with Sasuke. Maybe Sasuke says something harsh about Naruto's skills and Naruto, in his pride, decides to leave. Another could be that Naruto feels he's holding the team back in some way and leaves to train on his own in order to become stronger without being a burden. Or perhaps there's a mission gone wrong where Naruto is blamed for something he didn't do, and he leaves out of a sense of unfairness.
One possible scenario could be that all of Naruto's friends are killed in a great battle. He survives but is left alone, haunted by the memories of his lost comrades. He might then wander the world, a solitary figure, with his only company being the memories of the past.
One possible scenario could be Naruto exploring new jutsu by experimenting on his own chakra. Maybe he tries to combine different elemental chakra within himself in unorthodox ways to create a super powerful and unique jutsu. Another could be related to his physical endurance. He might experiment with training methods that push his body to the limit, like enduring extreme pain or fasting for long periods while still trying to perform at his best in combat simulations.
One possible scenario could be that he succumbs to the hardships in the village as a child. Maybe the villagers' hatred towards him is too much to bear, and he gets into a situation where he can't defend himself. Another could be that he's on a mission early on and it goes horribly wrong, perhaps facing an enemy far too powerful for his young self.