Why Did Mahiru Kill Fuyuhiko Sister?

Why Did Mahiru Kill Fuyuhiko Sister? In the game, we find out that Sato beat Fuyuhiko’s little sister to death with a metal bat. She did this because Fuyuhiko’s sister had been bullying Mahiru. Did Mahiru kill Fuyuhiko’s sister? At first she tried to just talk to the girl, but then the girl said she