Kaworu is betraying Seele by deliberately failing at his mission. That is, he was supposed to contact Lilith.
Why was Kaworu working with Seele?
Kaworu was sent to NERV by SEELE in order to advance their goal of Instrumentality through a Third Impact that would occur under their direction. In fact, Kaworu only changes his mind when he realizes it is in fact Lilith in Terminal Dogma, as by that point he is unable to start any sort of Third Impact regardless.
What was Kaworus purpose?
It is revealed that, like Rei Ayanami, Kaworu is an artificially created being, but rather than having the soul of Lilith, Kaworu has the soul of the 1st Angel Adam. As an Angel and a part of SEELE, Kaworus goal is to reach the bottom of the NERV facility, Terminal Dogma.
What was Kaworus plan?
SEELEs original plan to accomplish this was to make Kaworu the Seventeenth Angel, the carrier of Adams soul, merge with Lilith, causing the Third Impact. This would, with the help of thirteen Evangelion units, accomplish the Human Instrumentality Project.
Is Kaworu an angel in the rebuilds?
Kaworu Nagisa is the First and Thirteenth Angel in the Rebuild continuity. No angelic name has been revealed for him.