She asked Shinji to take Rei's ID-card to her the next day.

Isn't Shinji a pain? He is, isn't he?

The key is that Asuka abuses Shinji. So, rarely, Shinji flips and assaults Asuka. Then Asuka is surprisingly meek.

His synchronizing rate left nothing to be desired.

Shinji found it very difficult to adjust himself to life in the new school. However, the fact that he was an EVA pilot made him popular.