Shinji keeps his eyes averted from Rei’s gaze throughout
REI:“We leave in sixty minutes.”
SHINJI:“Do I... to pilot that thing again?”
REI:“Yes, you do.”
Azathoth: Shape of things to come for Shinji, really: his lack of social awareness driving him to seek comfort from those who won't provide it.
Kendrix: He is looking away because he's ashamed. Something at the back of his mind, probably his male protector's instinct, must be kicking the rest of his brain for more or less telling the pale, fragile looking girl over there to go and fight the horible monster alone.
Shinji buries his face in his knees
He spills words out to comfort himself without thinking.
SHINJI:“I don’t…want to.
Ayanami, you’re only saying that because you haven’t had any scary experiences piloting that thing.
I don’t want to – go through something like that ever again.”
REI (OFF):“Then sleep.”
Kendrix: Note that he, unlike the many who say that their relationship is "too distanced" would suggest, feels pretty comfortable spilling his inner feelings and fears to Rei. And this is before they were really close.
Rei's answers might come off as cold, but she is merely stating the facts.
And this is pretty much the point.
Shinji responds to that line
He lifts his head a little, opens his eyes and looks at Rei (Shinji was certain she would be sympathetic, so from his point of view, Rei’s words were completely unexpected…)
SHINJI (Back -surprised):“What do you mean ‘sleep’…?”
thewayneiac: The description of Shinji's reaction is unsusally detailed. The writers must have felt it vital for the animators to get this cut exactly right.
Kendrix: Thewayniac is right about the elaborate discription of the reaction shot.
Many say that Rei is too passive/submissive to spur Shinji into action, but in fact, she's very effective at doing just that - Shinji likes to put himself in the 'victim' position, to make himself believe that others force him to do things. He builds his argumentations to pilot or not to pilot EVA on the fundament of that belief. But in believing that he does only what others want, he'll never find out what he himself wants. He might seem weak-willed, but the truth is that Shinji, as Anno once tolf Tsurumaki during the making of Rebuild, has never actually done something he didn't want to do.
Rei, looks at Shinji and speaks bluntly.
REI:“I'll pilot Unit-01.”
Kendrix: Rei says this "just sleep" line because that's simply the way it will be, she doesn't accuse him of sending her to fight the monster alone because she was created to fight it, but this line has a much greater meaning to Shinji: It means he has a choice.
Both options have consequences, one is to be useless for everyone in Tokyo3, the other is the fear and danger of the battle, so there's no 'easy way out', Rei isn't shielding him from the hard reality in any way, but there IS a choice. Shinji didn't expect to be actually allowed to say 'no', he expected her to try and convince him with kind words.
In leaving him that Choice,with no authorities to hide behind, (a tactic that is also used by Mari (in Rebuild), though neither of the girls purposely used it as a means of manipulation) Rei allowed him to recognize what he truly wants...
Mr. Tines: Not for a minute wondering how come the first time he met Rei, their positions were revered...