^Her having romantic feelings for him?
If you come away from the show thinking that Asuka is not attracted to Shinji, then you failed to read the subtext, or even the outright text of what's onscreen, such as:
-the "Wall of Jericho" scene, where she clearly wanted him to come over to her side of the room and sleep with her, or at least make some kind of an advance.
-She applauds him and is charmed by his cello playing, which culminates in the very next scene of her wanting to kiss him. Her saying that she's bored is merely a way of her obscuring her true feelings for him--again, like the "Wall of Jericho" scene, she is giving him an opportunity to make a move and take their relationship to a higher level.
The above two points are confirmed in 22' when she expresses frustration in her mindrape sequence that he did not take her up on the romantic advances that she was offering him. Shinji was most likely too clueless and/or scared to recognize them as romantic advances and thus didn't "hold her" or "help her".
There's also the scene in EOE where she says to him: "If I can't have you all to myself, then I don't want anything from you!"