Third Impact; destruction and rebirth
Third Impact is the true purpose of the Eva series and SEELE's ultimate plan for humanity. This is the Human Instrumentality Project. For much of the anime and manga, the main cast of characters was led to believe they were fighting the Angels to prevent Third Impact. Only SEELE, Commander Ikari Gendou, Vice-Commander Fuyutsuki Kouzou, and Dr. Akagi Ritsuko knew the truth—Third Impact was the cover name, something to scare everyone else with. Since Second Impact killed half of the world's population, preventing Third Impact gave everyone a purpose, something to fight for. In reality, Third Impact was the same thing as The Human Instrumentality Project, which was SEELE's plan for the human race. NERV was its executive hand, made to carry out SEELE's plans of securing Instrumentality for humanity, and preventing the Angels' objective in reaching the same paradise.
Whether I cause Third Impact or not, either way I will cease to exist as an individual. Nagisa Kaworu, Stage 73
As Kaworu so keenly phrased it, Third Impact will allow humans to be "reborn in a new form, merged into one as a single life form." SEELE viewed this as humanity's next step in evolution. Enlightenment was to be achieved through uniting everyone's mind and soul. No doubt when this happened, there would be no more conflicts or misunderstandings.
This had no meaning to Kaworu, even though it was his destiny to bring about Third Impact. Existence as himself was important, and Third Impact would only serve to destroy that. Kaworu only valued his individuality. His human body and mind probably gave him human feelings he otherwise would not possess. And in the short time he was given freedom by SEELE, Kaworu liked his environment and he didn't want to go back or lose this freedom.
When he asked Shinji to kill him, he pointed out to Shinji that he's not dying for anyone's sake (and certainly not for Shinji's). In no way does he do it to save humanity. He leaves the world on his own terms, for himself alone, proving himself in the manga to be far more selfish (and in many ways, far more real).