One possible reason could be a mission. In many Naruto - related stories, missions often take characters away from their families. Naruto might have received a highly important and dangerous mission that requires him to be away from Kushina for a long time.
One possible plot could be that Kushina's departure makes Naruto more determined to prove himself. He might strive harder in his ninja training, using the pain of his mother leaving as motivation. This could lead to him achieving new levels of power at a faster rate.
One possible reason could be to protect Naruto from the hidden threats in Konoha. Maybe she discovers some dark secrets or plots within the village that she believes will endanger Naruto, so she decides to take him away.
Naruto would likely become more independent. Without his mother, he'd have to rely on himself more. He might also become more reserved as he has this emotional wound. His relationships with others, like Iruka Sensei, could deepen as he looks for that parental support elsewhere.
The relationship between Konoha and the Uzumaki clan might be further strained. With Kushina leaving, Konoha would lose an important link to the Uzumaki. And other Uzumaki members might see this as a sign that Konoha is not a safe place for them.
One possibility could be that Naruto discovers a long - hidden secret about his family that makes him feel betrayed. For example, he might find out that Minato and Kushina had made a deal with a dangerous enemy in the past that put the village at risk. This would be so against Naruto's values of protecting the village and his friends that he decides to leave them.
If Kushina leaves Minato for Naruto in fanfiction, it would completely change the Naruto universe's family dynamics. Naruto might grow up with a different kind of support system. Instead of the absent father figure of Minato, he could have a more present mother figure in Kushina. This could also change his relationship with the village. Since Kushina was an Uzumaki, her presence could lead to Naruto having an earlier understanding of his heritage.
One possible reason could be for Naruto's safety. Maybe she has to go on a dangerous mission and believes Konoha is the safest place for him. Another reason might be that she is forced by some powerful enemies who threaten Naruto's life if she doesn't leave him in Konoha.
Their relationship might start off a bit awkward as Naruto has only known Kushina through stories. But as they travel, they would gradually bond. Kushina would share her experiences growing up in the Uzumaki clan, and Naruto would listen intently, feeling a deeper connection to his roots.
He would likely become more self - reliant. Without Minato and Kushina's guidance, Naruto would have to figure things out on his own. He might make more mistakes at first, but those experiences would toughen him up.