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.
One possible reason could be that he feels misunderstood by his family. Maybe they have different expectations of him and he can't bear the pressure, so he decides to run away to Kumo to start a new life.
Adapting to a new ninja system could be a big challenge. Kumo may have different training methods, rules, and traditions compared to his home village. Naruto would need to learn and adjust quickly if he wants to survive there.
He could meet some rogue ninjas. These ninjas might either try to harm him or, in some cases, offer to help him on his journey. They might have their own reasons for being in the area between Konoha and Kumo.
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.
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.
Maybe he's running away from the pressure in the village. There are always high expectations on him, and he might feel suffocated and need some time alone to figure things out.
It could be that Naruto has some sort of conflict with the people in Konoha. For example, he might have been wrongly accused of something. So, he runs away to Kumo. In Kumo, he might meet new friends and allies who help him prove his innocence and also improve his ninja skills.
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.
Naruto could meet the Raikage in this fanfic. The Raikage, being the leader of Kumo, would surely take notice of Naruto's arrival. They might start off on a tense note, as Naruto is from a different village, but later develop an understanding.
Another reason could be for the sake of protecting the village. Maybe he discovers some sort of threat that he believes he can only face by leaving Konoha. He doesn't want the village to be in danger because of him, so he runs away to draw the danger away from Konoha.