In some fanfictions, it could be that Anko is influenced by an outside force or another character. For example, if there's a new villain who manipulates her emotions towards Naruto. Or perhaps Anko has some hidden insecurities that make her act out in this way. Also, the author may be trying to explore different relationship dynamics and use this as a way to show how Naruto would react to such a betrayal.
One possible reason could be a miscommunication between them. Maybe Anko feels neglected and then strays. Another reason might be that the writer wants to create a more complex and angsty plot.
Maybe she loves the Naruto world so much. The unique characters, like Naruto himself with his never - give - up attitude, and all the different jutsus and storylines in the original Naruto series make her want to explore more in fanfiction.
One possible reason could be a misunderstanding. Maybe Anko was involved in a mission that Naruto thought was unjust, and he misjudged her actions as being malicious. For example, if she had to capture someone Naruto considered a friend, even if it was for the right reasons from Anko's perspective, Naruto might hold a grudge.
One possible reason could be a misunderstanding. Maybe Anko thought Naruto was involved in something dangerous or against the village rules without having all the facts. For example, if there was some sort of strange activity in the village and Naruto was in the wrong place at the wrong time, Anko might jump to conclusions and attack him.
One possible reason could be unrequited love. Maybe Naruto has deep feelings for Anko, but she doesn't feel the same way. She might be focused on other things like her ninja duties or she could have feelings for someone else. Another reason could be that Anko betrays Naruto's trust in some way. For example, she might break a promise she made to him that was really important. It could also be that Anko does something that goes against Naruto's ideals, which makes him feel heartbroken as he had a different image of her in his mind.
Perhaps Anko has a personal connection to Naruto. Maybe she sees a bit of herself in him, like his determination in the face of difficulties, and this makes her feel a sense of kinship and thus the need to protect him.
He might also become more reserved in future relationships. After being cheated on by Anko, Naruto could be more cautious when it comes to getting close to someone again, always having that fear in the back of his mind that he could be betrayed once more.
Anko might develop a softer side through her interactions with Naruto. She has a tough exterior due to her past, but Naruto's unwavering optimism and kindness could start to break down her walls. She could become more open and trusting towards others in general.
One plotline could be that Anko takes Naruto on a mission to track down Orochimaru's remaining followers. Along the way, she teaches him about the different snake - related jutsu and how to counter them. Another could be that Anko tries to toughen Naruto up by putting him through extreme survival training. Maybe she takes him to a dangerous forest where he has to rely on his wits and new skills to survive.
One reason could be that Naruto has always been more attracted to those who understand his outcast past better. Sakura doesn't really have that kind of connection with him as she comes from a more normal background. So there's a lack of that fundamental understanding between them which hinders any romantic feelings.
It could be possible in fanfiction. Maybe Naruto discovers a different side of Anko that he's attracted to. They might get married secretly to avoid the chaos that would ensue in the village due to their unexpected union. But in the real Naruto storyline, their relationship is not at all hinted at in that way, so it's purely a fan - created idea.