Well, it might be due to some kind of mind - control or curse. Suppose an enemy put a curse on Naruto that made him see Sasuke's sister as an enemy. In the heat of the moment, without realizing the truth, he might have attacked her. Also, if there was some sort of prophecy or false vision that led Naruto to think she was going to cause great harm in the future, he could have been driven to kill her.
One possible motive could be a misunderstanding. Maybe Naruto was tricked into believing that Sasuke's sister was an immediate threat to the village. Another could be that she was somehow involved in a dark plot against Naruto's friends, and Naruto felt he had no other choice to protect them.
In the context of this fanfiction, Naruto could have killed Sasuke's sister because of a power struggle. If she was in possession of a very powerful and dangerous ability or object that she refused to hand over, and Naruto feared it would fall into the wrong hands. Or perhaps she was part of a group that was planning to overthrow the current leadership in the ninja world, and Naruto saw her as a key figure in that plan and decided to eliminate her to prevent chaos.
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.
One possible motive could be a dark magic or mind - control situation. Maybe an enemy has the power to control Naruto's actions and forces him to kill Sasuke against his will. Another could be a miscommunication where Naruto believes Sasuke has done something unforgivable, like harming the village in a way that Naruto can't overlook.
One possible motive could be jealousy. Maybe she was jealous of Naruto's growing power and popularity within the village. Another reason might be related to some dark family secret or a curse that forces her to take his life against her will.
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.
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.
Perhaps in a fanfiction where the world has been completely turned upside down. If Sasuke had been tricked into becoming an unstoppable villain who was about to destroy the entire ninja world, and Sakura was somehow aiding him (maybe under a genjutsu), Naruto might feel he had no choice but to stop them by killing. Another reason could be a broken heart. If Naruto loved Sakura deeply but she constantly rejected him and chose Sasuke, and then Sasuke and Sakura betrayed him in some way, his anger and pain could lead to such a drastic act.
A possible motive could be that Naruto discovers some dark secret about Minato that makes him feel betrayed. For example, if he finds out that Minato was involved in some unethical experiments that led to the suffering of many people. Or perhaps Naruto is tricked by a powerful villain who manipulates his emotions and convinces him that Minato is the root of all his problems.
One possible motive could be mind control. Maybe an enemy manages to take over Kakashi's mind and forces him to harm Naruto. Another could be a misunderstanding. For example, if Naruto was thought to be possessed by a powerful and dangerous entity that Kakashi believed could only be stopped by killing Naruto.
One possible motive could be that Sakura is brainwashed. Maybe an enemy uses some kind of mind - control jutsu on her and she becomes a puppet to kill Sasuke. Another could be extreme jealousy. If she felt that Sasuke was slipping away from her in some way, in a very dark and twisted version of the story, it could lead to her killing him.
One possible motive could be that Sasuke has been consumed by his thirst for power. In the Naruto universe, Sasuke has often been shown to be willing to sacrifice a lot for power. In this fanfiction set in the Wave arc, perhaps he sees Sakura as an obstacle to his pursuit of power, either because she tries to stop him from following a dark path or he believes she will hold him back in some way.