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.
It could be that Naruto is left behind as a punishment for some prank he pulled. While left behind, he meets a strange animal that has some connection to the Sage of Six Paths. Through his interaction with this animal, Naruto gains new insights into chakra and how to control it better.
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.
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.
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.
One possible plot could be that Naruto feels abandoned by Sakura after she chooses Sasuke over him. Naruto then goes on a journey of self - discovery, training harder than ever to prove his worth not just to Sakura but to the whole village. He might face new enemies alone and form unexpected alliances, all while dealing with the emotional pain of being left behind.
Perhaps there was a dark secret about Naruto's origin that was revealed in a way that made others fear him. For example, if it was discovered that he had some connection to a feared enemy or an ancient evil. This could lead to his betrayal as people's fear overrode their previous loyalty to him. Also, jealousy among his peers could be a factor. If Naruto was constantly getting stronger and more popular, some might have become envious and were easily convinced to turn against him.
One possible plot could be that Anko takes on a young and inexperienced ninja as her apprentice. She could start with basic physical training, like running through the forest while dodging various traps she sets up. Then, she might move on to teaching ninja techniques, especially those related to her own special skills in snake - based jutsu.
In some naruto secret training fanfiction, the training could be centered around Naruto's connection to the Nine - Tails. He might learn how to tap into the Nine - Tails' chakra in a more controlled and efficient way without the negative side effects. This could involve some spiritual journey within his own mind - scape where he and the Nine - Tails reach a new level of understanding and cooperation, leading to a huge boost in his power.
One possible plot could be that Naruto is sent to a secret training ground by an old sage. There, he learns unique jutsu that no one in the Leaf Village has ever seen. He might train in extreme conditions, like fighting against illusions that mimic the strongest enemies. This new training gives him an edge over his peers and he returns to the village a much more powerful ninja.
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.
In a 'Harry Potter left magic behind' fanfiction, the plot could involve Harry feeling guilty about all the destruction magic has caused. So he abandons it and starts anew in a remote place. He tries to build relationships with Muggles based on honesty. But as time passes, he realizes that magic is a part of him and he has to find a balance. Maybe he starts teaching some Muggles about the good side of magic in a very discreet way to help them better understand the world around them.