In the fanfiction, Naruto could be running away with Itachi because he wants to understand Itachi better on his own terms. The ninja world has its own view of Itachi, but Naruto believes there is more to him. By running away with something related to Itachi, like a personal item or a memory, Naruto can explore Itachi's true nature away from the influence of others. He can study and learn from it in solitude, without the interference of the village politics and the opinions of others.
Itachi might have entrusted Naruto with something before his death. And Naruto, being the person he is, feels that the only way to fulfill that trust is to run away from the prying eyes of the ninja villages. This could be a weapon, a scroll with important information, or a key to something bigger. Naruto doesn't want it to fall into the wrong hands, so he takes it and runs.
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.
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.
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.
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.
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.
Another reason could be related to a prophecy or a hidden mission. They might have learned about a prophecy that required them to leave Konoha in order to fulfill it. This could involve finding a powerful artifact or learning a special technique that could only be achieved by being away from the village. Their departure would then be a sacrifice for the greater good of not just Konoha, but the entire ninja world.
In the 'run away children story', sometimes children run away because of a lack of understanding or communication at home. Parents might be too strict or not pay enough attention to their children's feelings. The children then think running away is the only way to get noticed. Also, problems at school like bullying can lead to children running away. They may feel that they can't face the bully anymore and choose to leave.
A reason could be that Itachi is framed as a traitor to the Leaf Village in the fanfiction. Naruto, being the defender of the Leaf, would then see Itachi as an enemy and take action to kill him to uphold the village's safety and honor.
Another reason could be that she wants to explore the world on her own terms. In the fanfiction, Mirabel may be tired of always being in the family's protective bubble. She desires to see what lies beyond the village and the mountains, so she runs away to start her own adventure.
She could run away because of a broken heart. Maybe she had a relationship that ended badly, and she needs to get away from the memories. In the process of running away, she could meet new people who help her heal and grow as a person. This type of storyline often explores the more vulnerable side of fem Tsuna.