ROMANCE
As a young teenager going through her first experiences with feeling romantic love, Asuka tries to act mature enough to handle sexual relationships. In private, we see that she's really not so different than any other girl her age; she struggles with figuring out how to act on and cope with her newfound feelings.Normally parents set an example for their children and to act as guides through new experiences like first-time crushes. In Asuka's case, her mother was unfit for parenting and her father was not there for her. Her father set a very poor example for Asuka to follow: he carried on sexual relations with her mother's doctor in the room adjacent to hers. As a child, Asuka wouldn't know any better and would perhaps assume that all adults carried on this way and his actions would affect her judgement in the future.
After her mother's passing, Asuka wanted to grow up quickly and be seen by others as an independent adult. Although she's still a teenager, she's accomplished much but people still view her as a child. Asuka views sex as a way to be seen as an adult because in her mind, sex is something adults do. Her desire to be seen as an adult is compounded by the fact that she's developed physically and has already started menstruating. To Asuka, an older man as her lover or boyfriend would make people see her as an adult, which drives her to throw herself at Kaji on the night before their arrival in Japan. He rejects her, saying she's still a child, and she's unable to understand how he can think that way as she's now a woman and no longer a girl.
Asuka's affection for Kaji likely isn't solely as a means to be seen as an adult in the world she lives. I think she genuinely has a teenage crush on him and it's not hard to see why: he's handsome, suave, intelligent and cool. Asuka frequently talks about Kaji being her ideal man, follows him around, pesters him to go out with her and hangs onto him whenever she can. It's typical behaviour for a young girl in love!
To further her dislike for younger suitors, she actively dislikes the attention she receives from her many admirers at school. We see she has tons of love letters that fall from her locker and she crushes them underfoot. Yet, she begins to develop feelings for Shinji, someone her own age. I think that these feelings confuse and frustrate Asuka; she's supposed to be an adult who likes adult things, not a teenage girl who likes teenage boys. Shinji is submissive and self-deprecating and proud Asuka doesn't want to be seen liking someone so weak.
As time passes and Asuka grows closer to Shinji, her feelings grow stronger and she decides to try to act upon them. Being inexperienced, she asks Shinji if he wants to kiss her. She plays it off as something to do to pass the time and even acts disgusted by the kiss afterwards by running to the bathroom to wash her mouth out. However, we see later on that she's actually very upset by the fact that Shinji didn't hold her and didn't apprehend her underlying desires. I think she's so hard on Shinji because she wants him to become more assertive so that she can be comfortable with the idea of potentially being with him in a relationship.
It further frustrates Asuka that she can flirt with Shinji, but he doesn't act on her advances. There are several instances where she clearly dislikes the perverse nature of boys but once she becomes comfortable with Shinji and realises her feelings for him, she has little issue with showing off her body to him to get a reaction. Yet he never takes the opportunity to act and Asuka never understands why. Shinji clearly has an attraction and interest in Asuka but she doesn't realise that her abrasive attitude actually pushes him away. She takes his confusion as a lack of interest, which partially drives her depression later on in the series.