Evangelion is about kids who grew up with a fundamental violation of the parent-child bond that expressed itself in how they interact with others, their self perception, etc. In Shinji's case his relationship with his living parents is very detached, and he's always feeling like his only form of acknowledgment is when he's being a means to an end for his dad, and that he isn't really ever genuinely loved by anyone just for who he is. That's why his relationship with Kaworu messes with him so much, because he experiences what it's like to just be genuinely loved and valued just for being himself. That's why he always runs away from piloting, because he never believes that the connection is genuine, and he only ever pilots the Eva for others, but not for himself.
In Asuka's case, her mom always saw her literally as nothing but an accessory extension of herself like a literal doll. Asuka desperately wanted not to be alone, but ultimately her mom didn't kill her when she committed suicide, so she always felt like she was a failure to that connection and that she was replaceable. It's why she's super precocious and over-focused on her own performance, when she's passively really jealous of things like when Shinji & Rei can sync up and keep in step with one another, because she is compelled to force herself to remain in a situation no matter what it means. She never pilots the Eva for other people, she only ever pilots it for herself.
That's why the Evangelions are LITERALLY built with the souls of the children's mothers, and they're being piloted by blurring the mother-child ego barrier to the point that, like when they were in the womb the child and mother shared a single existence. It's where all the AT field and Ego barrier stuff gets its foundation for the ideas around the Human Instrumentality Project. That's the fundamental basics of how they pilot the Evangelions, and why those relationships are really central to the themes of the story. That's why when they get the umbilical cables cut, they have a limited time to remain powered, and everything involves intentionally pushing the pilots into survival mode and experiencing primal panic to sort of traumatize them into a place where they know exactly how Shinji is going to respond in order to facilitate the third impact.
When it comes to Asuka & Shinji's relationship, that's why there are so many awkward pieces, because Asuka is always pushing Shinji because she wants him to show the type of strong emotional reactions that she needs to be able to believe, and why she has a line in the original ending that she wants him ONLY if he promises to be 100% hers and no one else's. By the same extension, Shinji can't get closer to her like that because he needs her to just be gentle and show that she loves him regardless of how capable he is or isn't. They both need the same things but from opposite directions, and thus their tendencies make a negative feedback off of each other until Shinji gets totally focused on piloting and Asuka totally loses her ability to sync at all.
EoE dials in on that EXTRA hard, with tons of symbolic representations of that, but the ending scene is where that's extremely prominently expressed. For the first time, Shinji isn't holding back on his emotions and is letting all of his pain and anger out and he's choking her to death, which is the exact moment that Asuka finally really feels genuine with him and reaches up to gently touch his face. – And the second that she does, he breaks down crying and stops doing what he was doing and wraps his aggressive emotions back into his head, which sends that discomfort back into Asuka and she calls him disgusting which is exactly what is the equivalent to what Shinji doesn't need, and leaves them both where they started. They're stuck with each other but they can't find a way to exist with each other that gives both of them what they need.
It's a psychological examination around how there's a very particular type of coping mechanisms of that type of abuse can make circumstances where people are almost exactly the same, but just end up fueling pain in each other. The two different coping strategies are reversed to one another, and rather than filling each other they just accelerate that pain. It's depressing because no matter how much they do or how hard they try to help each other out, they always end up pulling those things back down around them. Deep down you can see that they're both reflections of their parents' inner pain that got passed along – and those are the moments when they're syncing with their Evangelions outside of having a power source. The anime just sets that up in a way where the emotions they go through are also what shapes the entirety of literal reality around them.
There are similar things going on with Dr. Katsuragi, Misato, Kaji, and the other adults in their own struggling stages of becoming adults to the children, while they're not in a place where they're totally past the messed up relationship with their own parents, but they're trying to do so anyway, and then there's Rei in the position of being a clone of Shinji's mom and also trying to figure out the meaning of her own existence and her emotions.
Following the emotional dynamics of the parent-child relationships into what makes all of the characters who they are is what will give the most insight into the really messed up and abstract parts of
Evangelion's endings, and also will help to give more context on why
Rebuild does what it does, especially with Asuka's character.
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