I have a lot of feelings about Shinji and Kaworu.
I know that Kaworu’s insertion has been criticized as deliberate and ridiculous yaoi-fodder, but I think that’s a really myopic view of his purpose in the series.
Shinji is cripplingly terrified of relationships with others. Though he has constructed this elaborate delusion where his self-loathing and isolation are a form of martyrdom, he is very self-centered, and desperately wants validation and security from those around him on his terms and under his control. Unfortunately, self-loathing and abandonment trauma kind of throw a wrench into any prospects for intimacy.
Kaworu fulfills Shinji’s desire for a safe, human connection. Since it has already been suggested that Shinji’s sexuality w/r/t women frightens and occasionally repulses him (see: all his interactions with Asuka, Rei, and Misato), Kaworu’s gender establishes him as uniquely nonthreatening. His professions of love elevate Shinji at the expense of Kaworu’s own identity and autonomy (“I was probably born to meet you”), making Shinji the center of his universe. Kaworu is full of gentle but boundless praise and love. He caters completely to Shinji’s selfish and unrealistic interpersonal needs.
Which is why Kaworu’s death at Shinji’s hands is so symbolically necessary. Kaworu is too good to be true. His existence as an angel is the ultimate betrayal, and a confirmation of Shinji’s deepest fears: that no emotional investment is without risk. When Shinji kills Kaworu, much to his own anguish, it is him finally and fully confronting this fact. He must kill his fantasies and distorted self-perception, because they have stunted him totally and because they harm him and harm others. He must realize that truly selfless love involves the death of self, and that while he envisions this as comforting, it is in fact horrifying: it is a personal, violent precursor to Third Impact and Instrumentality.