>>276738346He does it for the same reason he did it in the third impact. He thinks she’s going to kill him.
When you see the ghost of Rei you’re going to die. Shinji sees the ghost of Rei three times. When he first arrives to Tokyo-3. Then he gets in the EVA and the angel kills him, but the EVA goes berserk and brings him back to life. He sees the ghost of Rei again in the jump jet that comes to pick up his father in the cemetery. He is killed by the angel in the next episode. But the EVA goes berserk and brings him back to life.
In the third impact Asuka is killed, but she stays in the Eva, where what is left of Unit -02 can being her back to life. However this means she is NOT involved in the third impact. So whenever Shinji sees Asuka, he’s only seeing his version of her, who hates him. He begs this phantom not to kill him but she refuses, so Shinji strangles her and kills the world.
At the final scene Shinji sees the ghost of Rei, realizes that he’s going to die, believes ASUKA WILL KILL HIM and tries to kill Asuka first. But this is the real Asuka who loves him. Shinji gives up. Even if she does end up killing him, he can’t kill her because he loves her too. Also he realizes that he killed the world for nothing. It breaks him, and he weeps.