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.
Perhaps an enemy ninja has infiltrated the training grounds and causes chaos. Naruto is left behind because he's distracted by this enemy's actions, and the others don't notice he's missing at first. The enemy ninja then targets Naruto specifically, seeing him as an easy target while he's alone.
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 a powerful ninja from another village who sees Naruto's godlike powers as a threat to his own plans of domination. Since Naruto is already feeling vulnerable due to his family leaving him, this antagonist might try to take advantage of his emotional state.
In some cases, the antagonist could be a group of magical creatures that have been wronged by wizards in the past. They see Hermione as a representative of the wizarding world and when she is left behind, they try to make her pay for the past wrongs. These creatures could have unique powers and abilities that make them a formidable foe for Hermione.
It could be someone who took advantage of Kushina's leaving. Maybe a rogue ninja who wants to use Naruto's vulnerability to their advantage. They could try to turn Naruto against the village by making him believe that the village drove Kushina away.
It could be a rogue ninja who has a special ability to disrupt shadow clones. This antagonist might be jealous of Naruto's ability to use shadow clones for training and wants to stop him. Maybe he has a jutsu that can make Naruto's clones go berserk and attack him instead of following his commands.
It could be a new dark wizard who rises to power in the wizarding world. This wizard blames Harry for leaving and believes that his departure has made the wizarding world weaker. So the new dark wizard sends his minions to the Muggle world to force Harry to return to the wizarding world and face him, or else he will start causing chaos among Muggles which Harry has come to care about.
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 rogue ninja who has been secretly observing Naruto during his training trip. This ninja, jealous of Naruto's growth, decides to target him and the village he protects. He has some unique and dangerous abilities that even Naruto's new - found power will have a hard time dealing with at first.
It could be a rogue ninja from a hidden village that has a grudge against Naruto. This ninja might have a special jutsu that specifically targets Naruto's left eye during a fight, causing him to lose it.
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.