What is Asuka's core psychological wound?

She was abandoned — effectively — at the moment she most needed her mother. Her mother's break with reality withdrew the love Asuka needed at a formative age. The lesson she drew was that she must make herself impossible to reject by making herself impossible not to recognize — by being the best, visibly, undeniably.

She turned the need for love into the need for recognition. These overlap but are not identical. Recognition can be earned. Love must be given. She cannot control whether someone gives her love, but she can control her ability to be the best pilot. So she bets everything on that.

Why does her strategy fail?

Because it is contingent. When she is the best, she is temporarily safe. When others match or surpass her — particularly Shinji, who has no investment in competing with her — the strategy collapses. Her worth was supposed to be absolute (she is the best!) but turns out to be comparative (she is the best... except...).

And because recognition, even sincere recognition, does not reach the wound. She wants to be loved as she is, not valued for what she can do. But she has constructed an identity that makes receiving love impossible, because vulnerability — the precondition for love — is what she most fears.

What does the series do with this?

Anno does not resolve it cleanly. Asuka's story in End of Evangelion is among the most harrowing things in the series — a character whose constructed defenses are stripped away completely, leaving her entirely exposed. Whether what follows is destruction or something else is deliberately ambiguous.

The series does not offer her therapy. It offers witness — which is what she needed all along.