In Sherlock season 4, episode 3: "The Final Problem" why does Eurus want to torture Sherlock? What is her motive?
It is revealed that as children, Sherlock had redbeard as a friend. She wanted to be a part of it but that does not happen. She kills redbeard. But she does not do anything to Sherlock. That suggested to me that was the end of her revenge. Why does she want to torture Sherlock after 20+ years then?
She doesn't want to torture Sherlock, she wants to play with him. Specifically, she wants him to play with her. At least, that's what the childhood version of herself wants and it manifests in modern day as the torturous puzzling she sets up for Sherlock. Eurus lacks human emotion and, thus, doesn't see what she does as torturing her brother.