Him learning about Adamite Third Impact?
Btw, it should be noted that Asuka still has no clue about what actually could cause Third Impact, only that angels are involved. And that "the first angel" started Second Impact. Both are things Misato already knows, too (she was
there for Second Impact). Neither of them knows that it requires an angel to come into contact with Adam, that NERV has Adam in the cellar, that this is why the angels attack Tokyo-3 in particular, that EVAs are derived from him and that no wait, actually, that's Lilith, and 01 is derived from her... nevermind the whole souls thing. Or, well,
everything to do with Rei (which of course, given the stated romance option here, is highly reilevant). So there is actually still much to uncover.
Oh and one other thing:
This lack of self-awareness seems in-character for Asuka, though I must concede I find it a little tiresome.
Well, at the moment it isn't even that much lack of self-awareness
![Wink ;) ;)](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
. Because so far, well, there isn't even much in the way of just friendship between the two. Asuka is baffled anyone would jump into a murder beam for her, even as part of a mission, and doesn't want to be 'diminished' by someone dying for her, but that's it.
Unfortunately for your tiredness, realization
will be/remain her problem. Asuka will have few problems about liking girls... once she
realizes she does. That is because she has no problem with the general concept, but has a very strong and deeply embedded self-image...