In a Naruto fanfic where Naruto runs away from Kushina, it could be due to various reasons. Maybe he feels misunderstood. For example, Kushina might be too strict with him in the fanfic's storyline, not allowing him to pursue his own ninja way freely, so he decides to run away to find his own path and prove himself.
Perhaps Naruto feels that Kushina is being overprotective. He wants to prove his independence and go on his own adventures without her constant supervision, so he decides to run away.
Next, Naruto might meet new allies. He could encounter other ninjas who have also had run - ins with their families. They could form a group and train together, becoming stronger and more independent from their families.
He could meet other rogue ninjas. These are ninjas who have left their villages for various reasons, and they might be on a similar journey as Naruto. They could either help him or try to take advantage of his situation.
In a 'naruto runs away fanfic', one possible plot could be that Naruto runs away after feeling misunderstood by the village. He might go on a journey to find a place where he can truly belong. Along the way, he could meet new allies or enemies. For example, he might encounter a group of outcasts who are also on the run from different villages. They could team up and form a sort of 'runaway family' where Naruto learns new skills and perspectives outside of the Hidden Leaf's teachings.
He might miss out on some crucial training. Jiraiya has a lot of knowledge and skills to pass on, and by running away, Naruto could fall behind in his development as a ninja.
One possible reason could be that Naruto might be afraid of the intense training Jiraiya has in store for him. Jiraiya is known for his strict and grueling training methods, and Naruto, being young and sometimes impatient, might just want to escape that for a while.
Maybe he feels misunderstood by his family. In many Naruto stories, his family situation can be complex. If he's 'godlike', he might have powers that his family doesn't understand or fears, leading him to run away to avoid conflict or being treated differently.
He could be running away because of false accusations within the family. Just like how he was wrongly judged by the village in the original story, if his family wrongly blames him for something he didn't do, like stealing a family heirloom or causing harm to a family member accidentally, he might choose to run away rather than face their unjust wrath.
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.