There's a couple competing theories. The primary school of thought amongst Evangelion academia (based on some vaguely canonical Carddas trading card that was printed in Japan) was that Shinji was trying to see if she was still real. Within Instrumentality, Asuka would be unable to put up any resistance to the assault. However, in the real world, Asuka would be able to defend herself. I really don't like this one myself and the piece of merchandise that backs it up, besides being extratextual in the first place, doesn't have a clear direct line back to Anno.

Originally Posted by
Carddas
"Shinji renounced the world where all hearts had melted into one and accepted each other unconditionally. His desire... to live with 'others' — other hearts that would sometimes reject him, even deny him. That is why the first thing he did after coming to his senses was to place his hands around Asuka's neck. To feel the existence of an 'other'. To confirm rejection and denial."
Other theories that have been proposed:
- Asuka chose to return the world in order to die properly and was hoping Shinji would finish the job based on her experiences within Instrumentality.
- Since abuse is the only "love" that Asuka knows, Shinji lashing out at her is the "advance" that she had been looking for from him the entire time, and returned this gesture by stroking his cheek (the intimacy that Shinji has always wanted).
- My personal theory: during the first choking scene, Shinji finally decides he is tired of Asuka's emotional and sexual abuse, so he finally stands up for himself and chokes her out. When he washes up on the beach, having just experienced the trauma of Instrumentality and sees Asuka, the omnipresent "bully" in his life, Shinji, who now finally has a sense of self-worth, is willing to defend himself, and unwilling to live in a world populated solely by Asuka, finishes the job he started within Instrumentality.
- Regardless of your canonical interpretation of the scene, metaphorically, it hammers home the main theme of the show: even though humans often hurt each other, sometimes they choose not to. This is what makes human interaction worthwhile.
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