Michael Myers wants to kill Laurie Strode primarily because she became his target the moment he first saw her, sparking an obsession. In the original 1978 Halloween film, Laurie dropped off keys at the abandoned Myers house, which Michael was hiding in, and he began following her from that point on. Michael, who killed his sister Judith Myers years earlier, is portrayed as an embodiment of evil with no clear motive, capable of killing anyone, but he fixates on Laurie. His interest in her started as a random obsession that grew over time because Laurie proved to be resilient and difficult to kill, turning their dynamic into a deadly game of cat and mouse. Some interpretations also tie this to the idea that Laurie disturbed Michael's home (the Myers house), which motivated some of his killings in modern retellings. In older timelines, it was revealed Laurie is Michael's youngest sister, which added a family revenge dimension, but this was retconned in newer versions of the story where they are not related. The thrill of the chase and psychological torment seem to be key reasons why Michael delays killing Laurie outright, wanting to "play" with her first before attempting to finish her off.