Kurayumi kill sister from envy or from feel abandon.
Very obvious that Kurayumi fels envy or jealous, becuse her sister Ymaitsuki get more atention than Kurayumi herself, so feeling yourself abandon she get insane aka she a Sick Mind so she decide kiil her sister Yamitsuki and even Iratsuki who was Yamitsuki's friend maybe best friend, but in the end after bad deed Kurayumi understand that she make a very bad thing so she feels regret, too bad that is too late.