Unit 02; the scion of Adam
Kaworu was sent to NERV as the replacement pilot for Unit-02, since the Second Children, Souryu Asuka Langley, was losing her piloting abilities. All selections for Evangelion pilots fall under the Marduk Institute, though this system was later revealed to only be a puppet organization for NERV—every pilot was picked for a specific purpose. The first three Children were picked for their compatibility with each Eva's soul (this is more vague with Rei). Kaworu was picked directly by the committee, SEELE, in order to advance Human Instrumentality.
The Eva won't move unless you open your heart to it. [...] The Eva has a heart like your own. Closing your heart, you cannot synch with it. Nagisa Kaworu, Stage 58
Before even having Unit-02's core rewritten for him, Kaworu could synchronize with it at a very high ratio. This is only possible because, as the above quote describes, Unit-02 has shut its heart away, and because they are both scions of Adam. Since Kaworu's synch ratio with Unit-02 was very high, he is able to pilot it with prodigious skills, leaving Dr. Akagi Ritsuko to marvel, "Asuka was amazing—but he's better," during the battle with Armisael.
Even with his superior abilities, he could not defeat the 11th Angel, Armisael. The Angel could not be harmed with any of their conventional weapons, and whatever came in contact with Armisael was being fused with the Angel. After making first contact with Ayanami Rei, the Angel came after Kaworu, using his own weapon to sever Unit-02's left leg. At this point, the Angel invaded Unit-02, and although Kaworu could have stopped it, he chose to not act. Had he used his own A.T. Field to repel Armisael, he would have forfeited his role as SEELE's spy in NERV, giving away his true identity as another Angel.
A sacred province inviolate to anyone; the light of the soul. You should also be aware, it is the barrier of the heart that everyone has. Nagisa Kaworu, Stage 73
When the Angel delved deeper into Rei's heart and further corroded her body, and the situation was dire, Commander Ikari finally released the lock on Unit-01, and Shinji rushed to Rei's rescue. However, this only caused Armisael to turn its attention to Shinji. In order to save Shinji, Rei reversed her A.T. Field to trap the Angel inside of Unit-00 and then initiated self-destruction. While this all happened, Armisael leaked Rei's emotions into Kaworu, and shared her sense of loneliness with him. This would later be the sickening feeling he experiences in Shinji's presence, a by-product of Rei's love for Shinji.
After Shinji used Kaworu's room to escape having to face the pain of Rei's possible death, as well as him continuing to reject Kaworu's friendship and desire to be loved, Kaworu finally abandoned his respite—the brief experience with freedom away from his destiny. He met SEELE for the last time before setting off to do his duty. They talk about Ikari Gendou's wayward actions, and about mankind's fate.
NERV, originally formed as the implementing agency for SEELE, it was provided to carry out our scenario. Yet now it is becoming the personal agency of a single individual. SEELE, Stage 71
When he finally gained control of Unit-02 and descended down to Central Dogma, he is confronted by the only Eva pilot left. Shinji shouted at Kaworu, questioning why he tried so hard to be friends if he was an Angel, the enemy. Shinji asked if Kaworu was the one controlling Unit-02, as it was unmanned, its entry plug empty. Kaworu explained because they are both children of Adam, he could have physically fused with Unit-02 if he himself did not already have a soul. Since Unit-02's soul had shut itself away, he could easily control it. When Shinji was shocked at Kaworu having his own A.T. Field, Kaworu told Shinji everyone had one—that A.T. Fields are the walls that separate each individual's heart, and provided their individual bodies.