So, so many possible reasons. I refer to movies like End of Evangelion and Madoka: Rebellion as “make your own ending kits”; due to their constant use of symbolism and ambiguous dialogue, combined with a pathological aversion to explaining themselves, you can basically interpret them to mean whatever you want them to. If I may be allowed a bit of shameless self-promotion, I recently wrote a blog post doing just that. I didn’t specifically analyze why Asuka caressed Shinji, but going by the interpretation I adopted in my post, along with the mentioned card game translation, there are a few valid reasons why she did that.

This scene echoes one earlier in the movie, during Instrumentality, when Shinji and Asuka are arguing with each other about whose fault it is that they never managed to get close. I summarized the scene on my blog:

[Shinji] zeros in on Asuka in particular, isolating her in a dream version of Misato’s kitchen and fighting with her as Pen-Pen looks on, responding to her accusations that he didn’t know her at all that he couldn’t possibly know her, because she never talks about herself, and how unreasonable it is for her to expect him to know her when she won’t tell him anything. Rei appears and asks if he ever tried, and Shinji responds that he did, but couldn’t. Asuka asks how she could like someone who doesn’t even love himself. Shinji responds that maybe he could learn to love himself if she tried being nice to him, gets angry and smashes a chair, then wraps his hands around her neck and strangles her.

Shinji, who has spent a large part of the series being passive and self-loathing, finally gets angry and blames Asuka (and by proxy the other people in his life) for his inability to get close to others. Asuka and Rei respond, with some justification, that Shinji also has to take some blame; he avoids getting close to anyone because he fears being rejected and abandoned by them, as he was by his father.

In the end, Shinji manages to get over his fear of rejection and chooses to reverse Instrumentality and go back to the world where people are separate and can choose to reject or abandon each other. The card translation says that Shinji started to strangle Asuka because he wanted to confirm that rejection and denial exist once more. By going back to a world where rejection and denial exist, Shinji has admitted that he feared them, and faced that fear. He has confessed that Asuka’s and Rei’s accusations in the earlier scene were true, that he locked people out too tightly because he feared abandonment.

As Shinji strangles Asuka, she reaches up and caresses him, countering that although rejection and denial exist again, acceptance also exists again—people have the choice to accept others into their hearts, just as they have the choice to deny others. And with this, Asuka confesses that Shinji’s accusations in the earlier scene were true: Asuka resisted, at every level, accepting Shinji (and by proxy, everyone) into her heart, by yelling at him, demeaning him, and violently rejecting the rudimentary efforts he did make to get closer to her. But now that Shinji’s managed to stop fearing rejection from everyone, Asuka’s learned to stop rejecting everyone. Shinji knows he can’t passively wait for someone to accept him; Asuka knows that she can’t keep rejecting everyone.

Realizing that Asuka intends to stop rejecting him, Shinji breaks down in tears. Asuka responds “Kimochi warui”; to accept someone feels weird, foreign, and disgusting to her, because she’s always resisted it. At various points in the series, Shinji and Asuka almost manage to get closer—in Episode 15, Asuka compliments Shinji on his cello playing and then forces him to kiss her, but then violently rejects him by feigning disgust and running to the bathroom to wash her mouth out. Shinji doesn’t realize that Asuka was sincerely trying to get closer to him, or he realizes it, but won’t follow up because he’s afraid of being rejected. In Episode 22, after seeing her talk on the phone with her stepmother, Shinji tries to have a real conversation with Asuka about family, but Asuka is all pissed off because Shinij surpassed her sync ratio. In the final scene of End of Evangelion, they both realize their own culpability in the situation and decide to start trying to become people who are able to accept one another.