There could be a group of delinquent students in the high school. They might target Naruto because he is trying to be friends with Anko, who they see as their territory. They could try to bully Naruto and get in the way of his relationship with Anko.
Perhaps a strict teacher who doesn't like Naruto's unorthodox ways and Anko's rebellious attitude. The teacher might try to split them up and prevent them from participating in school activities together. For example, if they want to enter a school competition as a team, the teacher could create obstacles.
Perhaps Orochimaru from Naruto could be the main antagonist. He's always seeking more power, and in this fanfic, he might see the powers in 'The God of High School' as a means to achieve ultimate power. He could try to manipulate the events of the 'The God of High School' tournaments to his advantage, all while causing chaos in Naruto's world as well.
Loki could be a great main antagonist. He could be the mischievous student who's always causing trouble for the Avengers. He might use his magic to play pranks on them or steal their homework to make them look bad in front of the teachers.
It could be a jealous classmate. Maybe someone who has a crush on Armin and sees Annie as a threat to their relationship. This person could try to spread rumors about Annie to make Armin stay away from her.
It could be Orochimaru. Since Anko has a history with Orochimaru, and Nariko being Anko's apprentice, Orochimaru might see Nariko as a threat or a tool to get to Anko. He could try to manipulate Nariko into doing his bidding or try to steal her newfound skills.
Well, in a 'naruto and anko high school fanfic', perhaps Naruto is new to the high school and Anko is a bit of a loner. They meet during a school fight where Naruto tries to stop some bullies. Anko is impressed by his courage. Later, they find out they both have an interest in martial arts clubs at school. They start training together and form a bond that grows into a friendship and maybe something more as they face high school challenges like exams and rivalries together.
Perhaps a rogue ninja from another village who sees Naruto as a threat. This ninja could target Anko and Naruto during their training. He might be jealous of the Hidden Leaf's strength and think that if he can stop Naruto from getting stronger under Anko's teaching, he can weaken the Leaf Village. He could be a skilled fighter with unique abilities that pose a real challenge to Naruto and Anko.
Perhaps a jealous classmate who discovers Artemis's connection to the fairy world. This classmate wants to use that knowledge to gain power and popularity, so they start causing trouble for Artemis and his friends, trying to expose them to the wrong people or get in the way of their fairy - related investigations.
Gary could be a main antagonist. He might be jealous of Ash's popularity at school and constantly try to undermine him in Pokemon battles and in front of their classmates.
It could be a rogue ninja from a hidden village who has a vendetta against Konoha. This ninja might target Kurenai and Anko specifically because of their skills and knowledge, and Naruto gets in the way while trying to protect them.
It could be the school principal. The girl wants to put on a more edgy and progressive play that challenges some of the school's traditional values. The principal, being more conservative, tries to stop her from doing so. He or she makes it difficult for her to get the necessary resources and permissions, becoming the main obstacle in her acting journey in high school.