KAWORU:“You're so delicate, like glass, especially your heart.”
Dr. Nick: We'll discuss more about what exactly Seele is attempting in this episode soon enough, but here's one idea to ponder at this point: Did Seele send Kaworu to intentionally drive Shinji over the edge by betraying him? After all, in EoE they say in their ritual chant, "Through the destruction of the ego of Evangelion Unit 01's pilot, humanity shall now undergo Instrumentality", which suggests they are relying on mindbroken Shinji as a linchpin of their plan, hoping he'll choose instrumentality (or death, if you want to be negative about it) when offered.
Literary Eagle: The official book The Essential Evangelion Chronicle: Side B says that Kaworu approaching Shinji was not necessary for his mission, and came from a desire for a human relationship. In other words, Kaworu genuinely wanted to form a bond with Shinji, and was not following instructions from Seele to break him. I go into further analysis on Kaworu's motives (including more information from that book) in this article: Space Jesus, Take the Wheel. That article uses the French version of the book, however an English version of the book was released later.