Why do people who are obessed with someone sometimes want to kill the person they are obsessed with?
They become so obsessed with the person that they figure that they are the best thing for that person. Therefore they decide that if they can’t have the person no one else will be able to. Since they feel that they are the best why would the other person want to be with any one else. So the idea that the person would want any one other than themselves is an idea that makes no sense to them. So to prevent this from happening they lessen that possibility by killing the other person.