She could be driven by a sense of duty to her clan. If her clan has some old grudge or goal that requires her to go against Naruto, she would choose her clan over him. For instance, if the clan believes that Naruto's power will disrupt the balance among the ninja clans, Fem Sasuke might be pressured into betraying him to protect her clan's interests.
Jealousy could be a motive. If Fem Sasuke sees Naruto getting all the attention and praise while she feels overlooked, she might betray him out of spite.
Another possible motive is that she might be misled by false information. Someone could spread lies about Naruto being involved in something evil. Fem Sasuke, believing these lies, decides to betray him to prevent what she thinks is a greater harm.
Perhaps Fem Sasuke in this fanfiction has a different view of the world. She might believe that Naruto is a threat to her goals or to the future of the ninja world she envisions. It could also be that she has some deep - seated emotional pain that she blames Naruto for, and that leads her to kill him.
It might be for Naruto's own good. Sasuke may believe that Naruto is on a dangerous path that will lead to his downfall. So he captures him to keep him from making bad decisions, like sacrificing himself for the village or something similar. He wants to save Naruto from himself in a sense.
One possible motive could be if Sasuke was on a path of destruction that endangered the entire ninja world. Naruto, as the protector of peace, might see killing Sasuke as the only way to stop him. For instance, if Sasuke was about to unleash a powerful and uncontrollable jutsu that would wipe out many innocent lives.
Another motive might be jealousy. Suppose Naruto has something that the fem Kyuubi desires, like the love and respect of the people in the village. In that case, she could torture him out of envy, trying to make him lose those things that she covets so much.
Another motive could be a difference in ideology. If Percy believes in a different way of handling things compared to Artemis, and he feels that her methods are endangering the world or his loved ones, he might decide to betray her in order to stop her from following her current path.
One possible motive could be power. In some fanfics, Sasuke might be driven by an insatiable thirst for power and see Naruto as an obstacle. Another could be revenge, perhaps believing Naruto has wronged him in some way in that alternate story. Or it could be a matter of being corrupted by dark forces, which make him turn against Naruto.
One possible motive could be if Sasuke goes too far in his pursuit of power and becomes a threat to the entire ninja world that even Naruto can't reason with. Maybe Sasuke starts to kill innocent people without hesitation, and Naruto, as the protector of the village and the one who believes in peace, sees no other option but to stop him by killing. Another motive could be some kind of dark magic or mind control that makes Sasuke an uncontrollable force of destruction, forcing Naruto to take drastic measures.
It could also be a power play. In the Naruto universe, power is a big deal. Some might frame Naruto to get him out of the way in their pursuit of power. Since Sasuke has his own group of fans in the fic, they could be used as tools to achieve this by making it seem like Sasuke is against Naruto, when in fact it's all a setup.
Jealousy might be a motive. If Hermione is constantly outshining them in academics or getting more praise from teachers, they could become envious and turn against her.
One possible reason could be jealousy. Maybe fem Sasuke is jealous of Naruto's natural charisma or his ability to make friends easily. Another reason might be related to their different goals. If fem Sasuke has a very different view of how to save or change the ninja world compared to Naruto, it could lead to hatred.