There could be a scenario where Naruto was infected with a dangerous and incurable power that would endanger the entire world if left unchecked. Sakura, in a difficult decision, might choose to kill him to save everyone else. However, this would still be a very controversial and heart - wrenching situation within the context of the Naruto universe.
One reason could be jealousy. Suppose Naruto had achieved something that Sakura deeply desired for herself or for someone she loved, and in a fit of envy, she took drastic action. But this would be a very out - of - character move for the Sakura we know from the original series.
One possible reason could be a misunderstanding. Maybe she was misled by false information about Naruto being a threat to the village. Another reason might be that she was under some kind of mind control. In some fanfictions, dark magic or evil entities can take over a character's mind and make them act out of character.
A reason could be that Itachi is framed as a traitor to the Leaf Village in the fanfiction. Naruto, being the defender of the Leaf, would then see Itachi as an enemy and take action to kill him to uphold the village's safety and honor.
One possible reason could be that she might have underestimated Naruto in the past. She often belittled his abilities and dreams, but as she grew and realized his true strength and determination, she felt the need to apologize for her previous behavior.
One reason could be to create shock value. By having two main characters kill another important character, it grabs the reader's attention. Another could be to explore a very dark and alternate version of the Naruto universe. Maybe the writer wants to show how far characters could be pushed in extreme situations.
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 because of a dark curse. Suppose Naruto was cursed by an ancient evil. This curse slowly ate away at his sanity and made him view his friends in Team 7 as threats. As the curse took over more and more, he finally reached a point where he killed them. However, this would require a lot of backstory and character development in the fanfiction to make it somewhat believable.
One reason could be Sasuke's thirst for power. If he believes Naruto is the only obstacle in his path to ultimate power, he might be driven to kill him. In some fanfictions, Sasuke may be influenced by a dark entity that twists his mind into thinking Naruto is a threat that needs to be eliminated.
One reason could be jealousy. If in the fanfic, Sakura gets closer to someone else Naruto cares about, like Sasuke in a different way than he expected, it might make him hate her. For example, if Sakura teams up with Sasuke against Naruto's wishes in the fan - created plot.
Perhaps Sakura is in a state of extreme stress. Maybe she has a lot of pressure on her, like trying to save a village or a loved one, and Naruto's actions, which might seem reckless to her at the time, cause her to snap and hurt him without really meaning to.
One possible reason could be Sakura's constant pining for Sasuke. Naruto might feel frustrated that she's so focused on Sasuke when he's right there for her. In the Naruto universe, Naruto has always been a bit jealous of Sakura's love for Sasuke, and in fanfiction, this could be amplified to the point where he yells at her out of pent - up emotions.