I’ve never seen a protagonist - male or female - so effortlessly hide their ugly, unrepentant ego behind a veneer of warm compassion. Misato hits children, she hits wounded friends, she hits herself. My favorite Misato scene is when she just barely restrains herself from striking Shinji across the face, and slaps herself in redirected aggression. That’s her prerogative: redirected, impotent aggression, against the Angels and against herself. 

Misato’s a walking advertisement of her own desperation, which probably nets her more sympathy than she otherwise might deserve. Her violence aggrandizes her, but behind the display is total disempowerment. She tries to win back the control she lost during her childhood and it gets her nowhere. Her authority is skin deep.