The hedgehog's dilemma. Instrumentality is a state where there is no "other:" All of humanity is condensed into a single consciousness. One of the conceits of the show is that human beings, as individuals, are fundamentally alone; as such, we are doomed to constantly misunderstand one another, and in doing so, cause each other pain. Shinji ultimately realizes that this is a double-edged sword: hell is other people, sure, but you can't have happiness without other people, either. So you have to take the good with the bad, in other words. Thus, Shinji rejects instrumentality and emerges back into the world as an individual. Asuka makes that same choice, too.
Why does he try to choke her? Because he regrets his decision to come back. As the only other human being on earth, Asuka is the "other" -- kill her, and in effect, instrumentality is reinstated. But he can't do it for the reasons stated above. Asuka and Shinji are about as dysfunctional a pairing as you could imagine, but who would caress his cheek if she were gone? It's a small thing, but Shinji needs that. We all need that shit.
Caught in a existential Catch-22, Shinji breaks down (again). Depending on whether you watched the sub or dub, Asuka looks on and feels sick/disgust. She's stuck, same as Shinji -- but where he cries, Asuka feels only contempt for him and herself.
I used to think about this show way too much in high school and college
That was the interpretation I came to, anway.