One possible reason could be that he feels misunderstood. In the village, he has always faced discrimination because of the Nine - Tails inside him. People often look at him with fear and suspicion. So, he might run away to find a place where he can be accepted for who he is.
Sakura would be very worried. She has always cared about Naruto, even if she sometimes gets annoyed with his antics. She would probably try to find him right away, thinking that he's in some kind of trouble.
The villagers who once shunned Naruto might start to realize his importance. They would see how much they took his presence for granted. His absence could make them reflect on their past behavior towards him. Some might even join the search parties out of guilt or new - found respect.
However, there could be a group in Kiri who are more open - minded. They might be curious about Naruto and his abilities. They could welcome him and even offer to train with him, sharing their unique water - based jutsu knowledge in exchange for his knowledge of Konoha's techniques.
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.
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.
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.
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.