In some fanfiction, it could be related to a misinterpretation of character relationships. Maybe the author has a skewed view of Naruto and Sakura's dynamic and decides to create a tragic and unexpected turn of events where Naruto kills Sakura to show the breakdown of their bond.
Another aspect could be that the author wants to create a new and different storyline from the original. By having Naruto kill Sakura, it completely changes the direction of the story, allowing for new plot developments, new character arcs for other characters in response to this event, and exploring themes like guilt, revenge, and the consequences of such a heinous act within the fan - created world.