Academy City has created a no-win situation. They have created the Worst, a sister who embodies all of Misaka Network hatred. Because of their imperfections, sisters cannot feel hatred for anyone, even their murderer. Accelerator had begun to hope for forgiveness, but the existence of Worst destroys that hope. At the same time, Last Order is dying for Aiwass, and Worst wants to kill them both. If Accelerator will refuses to kill Worst, she will die from the bomb inside her body. It's a stalemate: if he does nothing, he, Last Order and Worst will die, and if he chooses to kill Worst, he has then failed to fulfill his promise to save sisters. Either choice will only lead to tragedy, where he will either die or be tormented by guilt from the rest of his whole life. And even if he somehow to save everyone, Academy City would still find a way to break him psychologically. Because of all these circumstances, he lost control and went on a rampage until Touma calmed him down (btw, in the third battle Accelerator succumbed).