REI (OFF):“Doctor Akagi is prepared to rewrite Unit-01’s personality data.”
He blinks once and speaks.
SHINJI:“Ritsuko-san is...”
Kendrix: ...which is certainly not to lose the semblance of a home he built for himself and, in his current mindset, the function that makes him important to others...
NemZ: I get the feeling this is actually Rei essentially telling him off, dismissing his whining and preparing to step up to the 01 piloting role she was meant for.
Captain Button: This scene gives me a feeling that part of Shinji's reaction may be territorial jealousy because Unit 01 is HIS Eva. Rei can't play with his stuff!
I also wonder if Rei is deliberately trying to prod him in that area as a trick to get him to stop moping around. But I can't really see Rei playing that kind of head game. But I can see Dr. Akagi trying to do so indirectly.