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Let me start by saying that Ayanami Rei isn’t even really a person. She’s a monstrosity made out Yui Ikari’s DNA. The connection between her and Shinji Ikari comes from Shinji being interested to her smell because it reminds him of his mother and the fact that his father is giving her positive attention instead of him. Her personality type in the original anime was a response to the love of typical emotionless and submissive anime girls, and why something like that wouldn’t work in real life. Both the manga and the movie versions replaced that with Shinji straight-up warming her up and making her more human than either her, her in-show clones, or the thousands of direct copies of her in other popular anime.
Rei is by far one of the worst girls in the show, maybe even just in anime altogether, because that was the point of the character. She’s the choice of people who want to escape from human interaction and want a pet to mold however they see fit.