Rei and Kaworu say they are "love and hope" for humanity.

>>161360291
Is this the dub? In the sub, they answered Shinji's questions: "who are you in my heart?" They answered: "I'm the hope someday we can understand each other" (Rei) "I'm the words 'I love you' " (Kaworu). They embody Shinji's hope to understand and love. Without counting his mother, Rei was the first person he tried to understand and the first one who conveyed it despite their misunderstanding (the smiling scene) and Kaworu who loved him and loved him back.
This is why he can continue to live in the world.

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>>161360518
>The only persons Shinji can understand and love are eldritch monsters
Shinji is a nice boy.

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>>161360291
Because humanity hoped to do cool things with them.