Kendrix: I wouldn't necessarily interpret "with eveyone" as something overearthly/lillith-ish. It could simply mean that, in Rei's opinion ALL her bonds define her, even the less significant ones.
Here, we also have the point where Shinji starts admiring Rei, at first, in an intellectual sense. (This is also stressed in Rebuild.)
He came to protect her, but now realized that this fragile looking girl he has seen covered in Bandages all the time is able to just go and do what she thinks must be done.
To Shinji, this is an impressive strong will. (Shinji shows similar admiration for Misato, and in Rebuild, for Asuka as well, though one could argue that while NGE Shinji didn't state it that obviously, Asuka's apparent strength might have been one of the things that made him fall in love with her.)
Now, Rei doesn't see that as impressive, it's not hard for her. She's simply fulfilling her purpose.
As she does, unbeknowsnt to Shinji, not consider herself particulary valuable or special, she uses a pretty sad, negative way to express this: "I have nothing else."
