This is my interpretation (I can go on forever about Evangelion), but if you look at "instrumentality," the entire concept is that we all become one. Kind of a happy place, where there are no boundaries between person and person, we are all part of one another at the same time, therefore you are never alone, but at the same time there is no longer such a thing as an "individual" or an "entity," just a big ocean of us.
And if you think of Evangelion as a whole as a metaphor for depression, instrumentality is kind of the ideal escape for the depressed. A perfect world. Heaven, as you will. Don't have to deal with scary social connections, don't have to deal with rejection, just exist in a harmonious ocean of embryonic perfection.
Shinji, as the poster child, chooses to reject instrumentality in the end. He chooses the imperfect world, where we each have our own thoughts and feelings, love and hate, but yet we are also individuals in control of our own lives. The human world, where we suffer, get our feelings hurt, fight, and yet that is what makes us human. It's kind of like the NEET breaking free of the safe and perfect hiding place which they never leave, yet also bars them from all the joys and wonders (and heartache) of the real world.
He strangles Asuka because it's an expression of him as an individual, of his love-hate relationship with Asuka as individuals. He has become a person again, and so he can reject her. In turn, Asuka caresses him, which is a sign that acceptance is also back. If they all remain merged, they wouldn't be able to reject each other ever again, but neither will they be able to accept each other, or there even be such entities as "Shinji" or "Asuka".
