Well, one possible reason could be a very extreme misinterpretation of Snape's hatred for Harry's father. If the fanfiction writer took Snape's grudge to an unrealistic level, they might write a scenario where Snape wants to destroy Harry as a form of revenge. But this is far from the nuanced relationship shown in the original books.
Perhaps he is under the influence of dark magic. There could be a spell or a curse that makes him lose his will to live. Or, in the fanfiction world, he might be bullied or persecuted to an extent that he sees no way out but to end his own life.
One possible reason could be his overwhelming guilt. Snape had a complex past, being involved in the Death Eaters and then switching sides. He might have felt that he could never truly be redeemed, especially with all the lives lost during the wizarding war that he had some part in, whether directly or indirectly. This guilt could have driven him to such a desperate act.
I'm not sure if there is such a specific 'Snape makes Harry kill himself' fanfiction. It's a rather dark and non - canon concept. Fanfiction can cover a wide range of themes, but this one seems extremely cruel and against the general spirit of the original Harry Potter series.
One possible reason could be his self - loathing. He has a complex past and has made many difficult choices. In fanfiction, the authors might explore his inner turmoil through self - harm as a way of expressing his pain. He may feel that he doesn't deserve any better because of his actions and mistakes.
One reason could be extreme guilt. Maybe he failed to save someone important and can't bear the burden of that failure. In some fanfictions, if he accidentally caused harm to his loved ones, like Aunt May getting hurt because of his superhero activities, the guilt might be overwhelming.
Maybe in the fanfic, Snape is written as having some hidden, truly evil motives that Harry discovers, leading him to kill Snape. For example, if Snape was secretly working for a new dark force even worse than Voldemort.
One possible reason could be extreme loneliness. In the Merlin universe, if Harry felt he didn't belong or was constantly ostracized, it might lead him to such a dark place. Another reason could be a sense of powerlessness. Maybe he was faced with a seemingly unbeatable foe and thought death was the only escape.
One possible reason could be the overwhelming burden of his destiny. Harry has faced so many challenges and losses throughout his life. The death of his parents, the constant threat of Voldemort, and the weight of saving the wizarding world might have made him feel so tired and hopeless that he contemplates taking his own life.
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.
Well, it could be that he has lost all hope. In the fanfiction world, if the situation becomes so dire that he sees no way out for himself or the people he loves. For example, if Voldemort manages to gain complete control and Harry Potter thinks his sacrifice by taking his own life might be the ultimate solution to break Voldemort's power. He might also be suffering from post - traumatic stress after all the battles and losses, leading him to this extreme decision.