Psychological + Emotional Trauma
It's easy to write off Asuka as being a bitch; she can be bossy, rude and temperamental and a lot of people don't like that about her. Much of her negative personality traits are a result from her experiencing psychological and emotional trauma as a child.Later in the series, we learn that Asuka as a child watched her mother, Kyoko, lose her sanity. Kyoko was admitted to a hospital where Asuka would come watch her play with ragdolls. Kyoko believed the dolls were Asuka and she would frequently talk to them, referring to the real Asuka as "that girl over there." She would usually dote upon the doll but there was at least one time where she became violent enough with the doll that she ripped its head off.
This alone is enough to cause Asuka to feel rejected and unloved. Why would her mother want to substitute her for a doll? Is she not good enough? This is further exaggerated when Asuka hears her mother tell the doll, "since your father doesn't need us, we should both die." It's bad enough to feel rejected, nevermind having it confirmed!
When Asuka learns that she's been chosen as the Second Children, she believes that she has finally accomplished something important enough that would certainly make her mother pay attention to her again. She believes that with her as a pilot, NERV would treat them both very well and they'd no longer have to rely on Asuka's father for support. Asuka runs to the hospital to share the good news with her mother but is met with a gruesome scene: Kyoko is hanging from the ceiling and the doll hangs next to her.
What must have gone through Asuka's head? If the doll had really been her, she would have died by her mother's own hands. A child's relationship with its parents is so incredibly vital to their health and wellbeing as an adult. Through healthy bonds, a child learns how to interact with the world around them, how to trust others and how to act. Kyoko's insanity left heavy scars on Asuka. With none of these feelings resolved, Asuka's feelings carry over into her teenage years.
Now older, Asuka's desire to impress her mother has changed to wanting to impress everyone else. She can't rely on other people and feels forced to act self-sufficient. She herself doesn't want to rely on anyone else so she tries her best to be seen as an independent adult who is capable of handling life on her own. When someone tries to help her, she becomes angry and defensive; needing help is a sign of weakness to Asuka, a threat to her capability to do things by herself. Offering her help is like saying "you are weak." This is why Asuka reacts so negatively in these situations. She hasn't learned that you don't always have to do everything on your own and that asking for help is a sign of strength. Without a parental figure in her life, she never learned how to control her emotions and never learned how to calm herself down.
Asuka also tends to be disconnected and withdrawn from others. She clearly wants to develop some kind of relationship with Shinji but has no idea how. When she makes an attempt to get closer to him and fails, she gets angry with him for not being able to understand her and what she wants. Of course, as Shinji eventually points out, he can't possibly know what she wants or try to understand her if she doesn't open up to him and explain herself.
Eventually her feelings catch up to her. As her self-image begins to crumble, her already overwhelming emotions get the better of her and she ends up in a deep depression. She shuts down completely until she realises that her mother has been protecting her all along from within EVA-02. In an allegory of just how much influence a parent has over their child's development, Asuka is able to break out of her depression once she knows that her mother never abandoned her. Her trauma seems at least partially resolved and she springs back to life.