Asuka hates Shinji because she feels she is inferior to him as a pilot. She resorts to seduction and her sexuality so that she feels she has some power over him. However, she ends up feeling even more angry and defeated because to her it looks like Shinji is immune to her charms. In her eyes, Shinji is defeating her all over again.
I want to add to this, that Asuka is unable to self actualize, and has struggled with this ever since her mother went though the EVA prototype experiments and came out of it as an aloof husk of a human being. She either couldn't or refused to recognize her own daughter. Asuka tries desperately to get her mother to acknowledge her, even submitting herself to the EVA program and earning the right to pilot the EVA her mother gave her heart and literal soul to, only discover her mother has hanged herself and she will never experience her acknowledgement again.
From that point on Asuka lives for the praise of others. If not for her pilot skills then for her brains. If not for her brains then for her body. The dysfunction of NERV only aggravates her issues because none of them are equipped to step into the role of parental surrogate either. Not aloof/alcoholic Misato. Not even Kaji, who's been her guardian for years is present in her life consistently enough to fill the role of a parent. Worse still, because he's such a mystery, Asuka has ascribed conflicting sets of expectations about him, both as a surrogate father, and as an object of sexual attraction. Single-minded, Kaji doesn't acknowledge either of those things and never does. So Asuka looks to Shinji and Rei for actualization, but they're just as damaged as she is, and Rei is barely even a whole person because of the human isolation of growing up with Gendo. When she attempts to live without the praise of others the circumstances of Kaoru on the base and her falling sync rate undermines her self-worth eventually leading to the psychic assault that essentially 'kills' her for the rest of the series.
Very good analysis and to all the ones who explored eva in this topic I enjoyed reading them. Also it's been a while but I'm confused over what exactly happened with Asuka's mother and what the deal is with that. If I'm remembering incorrectly it's that her father left her mother and the mother took it really hard so that's why she's left a shell of a human? I don't know how much Rebuild changes or retcons their backstory, and which source material you're going with since the original show left a lot of things ambiguous and/or unexplained. ---
