Michael Myers killed his sister Judith Myers when he was just six years old, and the reasons behind this act are complex and vary depending on the interpretation and timeline of the "Halloween" franchise. One explanation, as stated by John Carpenter, the director of the original 1978 "Halloween," is tied to an Oedipal or incestuous complex. Carpenter suggested that part of Michael's motivation stemmed from seeing his sister in a sexual situation with her boyfriend, which deeply disturbed him and triggered the violent act. This theory implies that Michael's killing was driven by a twisted form of vengeance and disturbed psychological impulses related to his sister.
Another perspective is that Michael Myers represents pure, inexplicable evil. Dr. Sam Loomis, a character in the film, describes Michael as having "the devil's eyes," devoid of conscience or understanding, implying that Michael kills simply because he embodies evil itself, without rational motivation. From this angle, the killing of his sister is the first act of this pure evil nature.
There are also suggestions related to narrative timelines or influences like the Cult of Thorn in some continuities, as well as various fan theories. But the most commonly accepted reasons are either the Oedipal revenge angle or the idea of Michael as an embodiment of pure, senseless evil.
In summary, Michael Myers killed his sister due to a complex mix of psychological disturbance (an Oedipal complex) and the characterization of him as pure evil within the "Halloween" mythos.
