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.
Additional Commentary
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.
Kendrix: I doubt he sees EVA 01 as "his toy" like Asuka does, he finds it very frightening and calls it a beast once - It's more that he feels useless and lost when stuff works out perfectly fine without him. His Dilemma is that while he is very afraid of the battles awaiting him, on some level, he wants them to need him (so he can keep his place in Tokyo 3).
Prologue!Arc Shinji reacts with horror whenever he's told he has a choice. (see ep 4) because it means he has to chose and can't blame the consequences on "they made me do it", and, not being very confident, he's sure those consequences will be bad.
This episode is a point where he improves significantly and comes one step closer to realizing that he's stepping into that big mecha because he wants to. He isn't forced, really- Rei could do it instead. It's just that Shinji doesn't want Rei to get hurt in battle/ doesn't want to be useless/ doesn't want to lose the small home he's estasblished for himself.
As for the brainwashing thing, I think Rei is merely stating the factsof what is going to happen/ the logical consequences of Shinji's actions, and doing so quite neutrally - She doesn't say "Stay here, or do you want XY to happen?", she says "Well, then leave if you want. We'll just do XY."