Well, 'Naruto: The Forgotten and His Harem' is a great one. It shows Naruto being left behind by his peers in a way that makes his character growth more impactful. As he is left behind, he starts to attract a group of female characters who see his potential. 'Left in the Shadows, Harem in the Light' is also a good read. In this fanfiction, Naruto's situation of being left behind is used as a catalyst for him to create his own unique path and draw in a harem of supporters and friends. And don't forget about 'Naruto's Lonely Start to a Harem Ending', which details how Naruto's initial loneliness due to being left behind turns into a harem - filled adventure.
One reason is for character development. By having Naruto be left behind, it creates a situation where he has to grow and change on his own. And the harem aspect adds an interesting dynamic, like in many stories where a character who is initially an outcast attracts others. It can also add drama and tension to the story.
As he grows up, Naruto could become very angry. He might develop a sense of abandonment and this could fuel his determination to become stronger. He would want to prove himself to his mother, wherever she is. In this fanfiction, his anger could be a driving force in his character development.
It could be a jealous fellow trainee. This person might spread false rumors about Naruto, which leads to him being left behind in training. The jealous trainee doesn't want Naruto to get stronger and be more popular.
Maybe Naruto is left behind in training because the instructor misjudges his abilities. As a result, Naruto starts training with a retired ninja who teaches him some old - fashioned but effective techniques. This gives him an edge when he finally rejoins his group.
Well, it might be about Naruto growing up without Kushina's presence. Maybe he has to face challenges alone and discovers things about his mother in the process.
One possible reason could be that Kushina was forced to leave Naruto due to some external threat she thought would endanger him more if she stayed. For example, if there were powerful enemies after her and she feared they would use Naruto to get to her.
I think Minato could also be a main character. As Naruto's father, he might play a role in Naruto's life even though Kushina is absent. He could be a guiding figure or a source of mystery for Naruto, especially if Naruto discovers things about his father in relation to his mother's absence.
A possible storyline is that Naruto starts to suspect that there was a darker reason for his parents leaving him. This could lead to a conflict within himself, whether to forgive them or not. He could also meet other orphans in the village and form a sort of support group. They could work together to change the village's perception of orphans. Another idea is that Naruto discovers a secret about his parents that puts him in danger, and he has to fight to protect that secret while also coming to terms with his feelings of abandonment.
Perhaps in this fanfiction, Naruto's family leaves him because they fear his godlike abilities. Naruto then has to prove that he can use his powers for good. He could start by helping the villagers who once shunned him. This would lead to a series of events where he gradually gains the respect and understanding of those around him, despite his family's absence.