One possible motive could be revenge. Bellatrix killed Sirius, who was very dear to Harry. So in the fanfiction, Harry might be driven by the intense desire to avenge Sirius' death.
One possible motive could be a dark magic influence. Maybe some powerful dark wizard or dark artifact has corrupted Harry's mind, making him do something completely out of character like killing Cedric. For example, the Imperius Curse in a more insidious form that even Harry is not fully aware of could be at play.
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.
Another motive might be related to a dark object influencing her. If Hermione came across a cursed object, like a dark locket that amplified negative emotions such as envy or fear, it could drive her to kill Harry. Maybe she started to envy Harry's fame and the special attention he always got, and the locket pushed her over the edge.
One possible motive could be that Snape is still deeply influenced by his loyalty to Voldemort in this fanfiction. Maybe Voldemort has some hold over him that forces him to do the unthinkable. Another reason could be a misunderstanding. Snape might believe that Harry has turned to the dark side or is about to, and he decides to take preemptive action to stop what he thinks will be a great evil.
One possible motive could be that Harry is under the influence of a dark spell or curse that makes him lose control of his actions. In some fanfiction scenarios, dark magic can overpower a character's true nature.
Another motive could be related to Bellatrix's loyalty to Voldemort. Maybe she suspects Hermione of something, and this is her way of getting a reaction out of her. She could be trying to unnerve Hermione to see if she gives away any secrets or shows signs of being involved in something that Bellatrix or Voldemort would be interested in.
In a 'Harry Potter kills Lucius Malfoy' fanfiction, the motives could be complex. It could start with Lucius's long - standing enmity towards Harry and his family. Harry may have reached a breaking point after all the years of Lucius's attempts to undermine him. Additionally, in the context of the wizarding war, if Lucius is seen as a key figure in Voldemort's regime, Harry might view his death as a strategic move to weaken the Dark Lord's forces. It could also be a way for Harry to assert his own power and dominance over the Malfoy family, who have always looked down on him.
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 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.
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.