A simple reason could be to escape a dangerous prophecy. Maybe there's a prediction that they will cause great harm to the village if they stay, so they run away to figure out how to change their fates.
Perhaps they run away because they are framed for a crime they didn't commit. The village elders turn against them, and they have no choice but to flee. On their journey, they search for evidence to clear their names. Naruto might be using his positive attitude to keep the group going, Sasuke with his determination to find the truth, and Sakura with her loyalty to the group, not letting any of them give up.
One possible plot could be that they run away from the Hidden Leaf Village to avoid a powerful enemy that is targeting them specifically. Maybe this enemy has some vendetta against them because of their unique abilities or past actions. They might have to rely on each other's skills and their friendship to survive in the wild and find a new place to call home.
Well, they could embark on a journey to discover a hidden ninja village that holds the key to a powerful jutsu. Along the way, they might face various challenges like traps set by rival ninja clans. And Naruto would probably be the one to keep everyone's spirits up with his positive attitude.
For Naruto, running away might make him more determined to prove his worth and protect his friends. He could learn to control his Nine - Tails chakra better in the face of danger outside the village. Sasuke may start to trust Naruto and Sakura more, realizing that they are his true comrades. Sakura, on the other hand, could become more independent and confident in her abilities, not just relying on Sasuke and Naruto but also being able to take charge when needed.
A plot could be that they are being hunted by a powerful and evil ninja organization. So they run away to gather strength and allies. Naruto might try to convince some of his old friends from other villages to join their cause. Sakura would be constantly worried about their safety but also determined to fight back.
Perhaps he is running away from danger in Konoha. There could be a threat that he believes he can't face directly in the village, and he thinks Whirlpool might offer some sort of sanctuary or a way to become stronger in relative safety.
Maybe he's running away from some kind of danger or threat in his home village. There could be a group or an individual after him, and he believes that Kumo would be a safer place. It could also be related to some political unrest in Konoha that makes him feel like he has to leave, and Kumo seems like a viable option.
They might run away to avoid a conflict that their villages are about to be dragged into. Naruto and Sasuke, being the powerful ninjas they are, don't want to be used as tools in a war, so they decide to run away.
Perhaps Naruto discovers something about Itachi that the rest of the world doesn't know and he needs to run away to protect that secret. It could be a powerful jutsu or a message that could change the balance of power in the ninja world.
One possible reason could be fear. Minato is a very powerful shinobi, and Naruto might be scared of him for some reason. Maybe he has heard stories about Minato that made him afraid.
In fanfictions, Naruto could run away from his family due to emotional abuse. If his family members constantly put him down, criticize his abilities, or make him feel unworthy, he'd likely want to escape. Also, if his family is involved in some political intrigue that he doesn't want to be dragged into. For instance, they might be making deals with other clans that Naruto disagrees with. Additionally, if there is a new family member introduced, like a step - sibling who is favored over him and he feels unloved, that could prompt him to run away.