
Short answer: Realizing that Asuka was with him at the end of the evangelization, Shinji smothered her because after they turned into separate human bodies, Shinji still hated how Asuka had hurt him by exposing all her weaknesses while she were still a being.As he strangles her, he cries because he feels guilty that he now fully understands Asuka why the two went through the instrumentality project.
Let's go through the events that took place during Third Impact to find more details on why Shinji decided to choke Asuka. Let's go!
What was Shinji going through during Third Impact?

Just before Third Impact took place, mass-produced EVAs attacked Tokyo-3. By this time, however, Shinji had already decided to leave NERV. He decided that flying an EVA brought him only pain and sadness. He didn't want to go back to EVA as much as possible and who could blame him? Just the fear of having to fight an angel would be enough to make you hesitate. And let's not forget the pressure that Misato and the others constantly put on him. We would have collapsed under all the pressure if I was Shinji too.
Also, during this time, Shinji sees people he knows die, such as Misato and Kaji. With all this on his mind, we totally understand why Shinji didn't want to pilot EVA Unit 01 and just sat there by himself. That was too much for a 14-year-old. However, his mother's soul is taking over the EVA and has given Shinji a sign that there is still hope. He decides to pilot it, and the EVA takes to the skies with new wings on its back. What Shinji awaited, however, was the sight of his friend and comrade being eaten by mass-produced EVAs.
This had another major impact on Shinji's heart. He couldn't accept that Asuka was dead. I mean come on, anyone would be shocked just to witness the death of their friend. But Shinji knew he had to accept reality, and when Shinji finally acknowledged that Asuka had died, he felt severe mental pain, causing Eva Unit 01's sync rate to increase. Somehow, the Longinus spear returned to earth and responded to Eve. Unit 01 is going insane. The Spear, the mass-produced Eva, and the Eva Unit 01 became one, forming the Tree of Life. Shinji is living through some kind of scenario in his mind at the Tree of Life and as a result, Rei comes to the conclusion that it was Shinji's wish to live in a world where there is no pain. Therefore, the Human Instrumentality Project began with Rei absorbing the Tree of Life and creating an Anti-A.T. Field strong enough to destroy all human forms. All humans become LCL and are gathered into one form, making their consciousness one.
Shinji then immediately regrets wanting his version of Human Instrumentality. because Shinji observed that instrumentality was a lonely way of existence. He understood that his past associations and relationships in the world before instrumentality brought him true happiness. So Shinji, even at the cost of being injured again, begged for another chance to experience that bliss of being with people, and chose to reject instrumentality in order to allow himself that chance. And so, Shinji eventually reverted to his human form and returned to Earth. The last scene shows him strangling Asuka without explanation.
What was Asuka going through during Third Impact?

Unlike Shinji, Asuka did not survive when Third Impact began due to Asuka fighting the mass production Evas. While her skills at piloting the Evangelion were impressive, she fought not just one unit, but nine. Eva Mass Production was outnumbered and was able to win by taking her unit Eva A.T. Fields replicated a Longinus spear and ended up poking himself in the eye with it. After that, she was incapacitated by the replica spear and the mass production of the Eva brutally ate her alive until the internal organs of Eva Unit 02 came out. Asuka's last words were "I'll kill you", meaning her resentment towards Eva Mass Production was huge. Her greatest wish here is the one that enabled her to return to human form after completing the Human Instrumentality Project.
How Shinji and Asuka influence each other

Throughout the series, Shinji's relationship with Asuka is very complicated due to the two having opposite personalities. Shinji is a rather passive and cowardly person while Asuka is brave and her ego is very high. Although the two have opposite personalities, Shinji sees Asuka as a brave and inspiring woman. As a result, Shinji uses Asuka as an escape route and as a source of his need for affection, just as Asuka uses Shinji as a source of attention and validation that she is awesome and independent. Asuka and Shinji like each other, but when things go wrong, they don't communicate. It's because of her self-loathing.
Why is Shinji choking Asuka?

At the end of Evangelion, not only does Shinji strangle Asuka in the final scene of the film, but before Third Impact begins, there is another scene where Shinji angrily strangles Asuka. Few people talk about the scene where Shinji strangles Asuka before Third Impact. Let's separate the two and explain each part.
Just before the start of Third Impact:

This scene played out in Shinji's mind after he transformed into the Tree of Life with the unit Eva 01. In Shinji's mind, we see Asuka sitting in Misato's apartment. Shinji approached her and spoke to her, asking her to help him. As we mentioned earlier, Shinji uses Asuka as an escape from his fear of abandonment and for the affection he craves. Asuka rejects Shinji because she doesn't want him to use her as an escape. Asuka then bombards Shinji with truths about all of his weaknesses. She corners him and even pushes him. Shinji hates the way she treats him and responds by strangling her. At this point, Shinji's version of Human Instrumentality began.
Final scene/post-third impact:

As we mentioned earlier, Shinji regrets wanting his version of Third Impact, so he wants to return to human form. Shinji believed that human instrumentality was a solitary form of existence because many aspects were removed as human consciousness became one. Shinji just wanted one more chance to live as a human, even if he got hurt again. Afterwards, Shinji managed to become human again and returned to Earth, where he ended up lying next to Asuka. Remembering all the pain she had caused him, he suddenly strangled her. But when he strangles her, he cries. Because before they became human again, they were one being and understood each other perfectly. Shinji feels guilty for hurting her, but hates that she knows all of his weaknesses.
Why was Asuka stroking Shinji's face?

When Shinji strangles Asuka after becoming human again, Asuka responds by stroking Shinji's face and saying "How disgusting". This is because Asuka finally understood Shinji when they were one being during instrumentality. All the hurt and pain he was going through, Asuka felt it and understood it too. When Shinji smothered her, she was simply stroking Shinji's face to let him know she was real, as well as an act of affection and/or pity for Shinji. While stroking his face, Asuka says her famous line so Shinji knows and understands that she is the real Asuka.
Our final thoughts:
Shinji regrets his version of Third Impact because he finds instrumentality a lonely way of life. Shinji realized that he wanted to become human again and return to Earth. After that, he landed next to Asuka who was lying on the beach and suddenly strangled her. This action meant Shinji was furious that Asuka knew all of his weaknesses. He was also angry at how she was treating him, even though he was only asking her for help. However, Asuka responded by stroking Shinji's face, which was a sign that she was real and that she finally understood all the pain and suffering Shinji was going through.
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