It could also be a matter of misinformation. If she is fed false information about Naruto, perhaps that he is planning something bad for her or the world she cares about, she might choose to betray him. In the world of Naruto, misinformation and misunderstandings often play a role in the relationships between characters.
Another aspect could be related to her past or origin. If she has some hidden memories or a secret agenda tied to her existence as the Fem Kyubii, it could lead her to betray Naruto. For example, if there are some dark forces that are controlling or influencing her from her past, she may be forced to turn against Naruto against her will in a sense.
Naruto would likely be initially shocked. He has always considered the Kyubii as a part of him and a friend in some ways. So the betrayal would be a huge blow to his sense of trust.
One possible reason could be power. Maybe in the fanfic, there's a new source of power that Tsunade wants desperately and Naruto stands in her way to obtain it. So she betrays him to get to that power.
One possible plot could be that Naruto discovers some dark secrets about Konoha's leadership. For example, he might find out that they were involved in unethical experiments in the past. This discovery could make him feel betrayed first, and then lead him to take actions that Konoha sees as betrayal, like refusing to follow orders or even teaming up with an enemy of Konoha who he believes has a more just cause.
One possibility could be a misunderstanding. Maybe Kakashi is framed for something that makes Naruto believe he has betrayed him. For example, an enemy could use a clone of Kakashi to perform a heinous act, and Naruto witnesses it without seeing the full picture.
One possible reason could be that Naruto discovers some dark secrets within Konoha. Maybe he finds out that the village elders have been using him all along, not truly caring about his well - being but only his power as a Jinchuriki. This realization could be so shocking that he decides to turn against the village.
One possible reason could be that it goes against the original dynamic between Naruto and Sasuke. In the original story, their relationship is based on a deep male - male bond of rivalry and friendship. Changing Sasuke to a female might disrupt that established connection.
One possible plot could be a power struggle. Maybe in a world where different fictional universes collide, Naruto God represents a certain power balance. Wonder Woman, perhaps influenced by some external dark force or a misunderstanding of Naruto God's intentions, decides to betray. This could lead to epic battles between their respective allies, with the fate of this combined fictional universe at stake.
One reason could be a miscommunication. Maybe a misunderstanding between them leads Arturia to think Shirou has done something unforgivable, so she betrays him.
One possible plot reason could be discrimination. In the Naruto world, there are often biases against those with different abilities or appearances. If Fem Naruto is constantly facing unfair treatment in Konoha due to her being a female version of Naruto, she might decide to leave. For example, she may not be given the same opportunities as male ninjas in training or missions. Another reason could be a search for identity. Maybe she feels that she can't truly be herself in Konoha and needs to go on a journey to discover who she really is away from the village that has so many expectations of her.
It could also be a misunderstanding. Hinata might be framed as a traitor. Some false evidence could be planted that makes Naruto and his friends believe she has betrayed them. This would lead to a lot of drama and conflict in the fanfiction as Naruto struggles with whether to believe Hinata or the evidence against her.