Evangelion musings. Manga and anime. Spoilers duh.
Shinji and Asuka are the last two people that should have ever met. They're completely incapable of having any kind of relationship even though it's clear they come to like each other on some level.
Shinji is desperate to be loved deeply by somebody. The only people he's ever truly loved were his parents and one of them is "dead" and the other completely abandoned him to strangers. The people that raised him were nice but they didn't love him. As a result he thinks giving his love will hurt him so while he wants it, he can't give it. He's a coward but it's understandable why.
Asuka is in dire need of someone to love her as a person and put her first in their life. She never met her father because he was a sperm donor and she was only born to show up her mother's rival that stole her love and had a plain daughter with him. When her mother loses part of herself Asuka feels completely alone and builds up her shell to be strong and tough so no one can ever hurt her again.
In a typical anime they could magically fall in love and fix each other but in Eva their problems are such that they can't help each other, only hurt one another when they try.
Asuka needs someone to break her shell and care for her and Shinji needs someone to love him but Shinji's timid nature keeps him from breaking through and that only serves to make Asuka angry because she gives him chances to flirt and be more. Showing off her body to him at the pool, the kiss challenge and lying with him in bed. When she later sees Shinji in her mind after all this stuff these are her thoughts:
That specifically reminds me of her getting into his bedding. After she falls asleep and mutters for her mom, a sign she clearly needs comfort, Shinji won't even put his arm over her, he just moves completely to the other side of the room and leaves her alone.
Later during instumentality in the kitchen it's pointed out that Shinji doesn't really care for Asuka because she's Asuka. He just wants her to care about him to fill his void. She could be anyone. He's selfish in a way expecting from her what he can't or won't give back. It's why he got on with Kaworu better despite being straight. Kaworu's love isn't hard earned like Asuka's, it's unconditional and given freely for none from Shinji.
Neither of them are bad in this situation. Shinji is afraid of Asuka and as much as that sucks for her it's not without reason. She's abrasive and mean a lot. Can you blame a broken 14 year old boy for being severely intimidated by an attractive girl who's partly a bully? He'd have a hard enough time if she were a total sweetheart. You can't really blame her though because her wall is there for a really good reason and she gives Shinji easy chances to breach it but he just sits on his hands and does nothing to help her.
After Shinji and Asuka emerge from the sea of LCL alone Shinji goes back to trying to choke her like he did in the kitchen when she completely rejected him. She touches him to show that something is different now. I don't know if you can say she understands him now because she clearly didn't in instumentality but there is a change because for once in that moment Asuka is tender and kind to him. These two broken people were the only two so shut off that they rejected universal oneness of humanity and they are wholly incompatible and unable to live together happily . Asuka is disgusted at everyone besides them for staying together. Asuka and Shinji are together but they're still alone.
I find myself being able to relate to Shinji a little. I've talked about my "Dream girl" on this board before. The one I knew since 13 and had a major chance with that married the guy she got with after. My key point in those postings was that I was a coward that couldn't make a real move or make something official even though she gave me chance after chance. I was so close to what I wanted more than anything and what I still find myself wanting sometimes and I couldn't do what I needed to to have it.
You know who I feel real bad for? Misato. She's Shinji's stand in mother and she's great at it. Shinji isn't just a job to her, she wants him to be happy and loved and she makes great progress until things go bad. I think it's all after Kaji dies. She seems to lose her confidence in her ability to care for Shinji and falls onto her own personal crutch of using sex to connect and motivate. The world beat her and Shinji to the point that her motherly efforts weren't enough. It's even worse in the manga because we get shown what Shinji really feels for Misato earlier. When Shinji gets absorbed by Unit 01 and becomes afraid of what the melding of the Eva's mind and his mother's soul has created he screams for his mother and out of the thing to grab him and pull him back to reality isn't a form of Yui or even Rei, it's of Misato. She was a great woman who did her damndest to love and fix this little boy and the word crapped on her efforts and the both of them.