Shinji:“No … I can't! I can't pilot something like this!”
Sephizim: I like the brief moment of hesitance here. I always felt like Shinji is at war with himself in a way. His nature as a doormat is to just go along with things, just because he prefers to avoid conflict. However, this is something he absolutely doesn't want to do, not only because it is completely unknown to him, but due to his disappointment that Gendo only called him to do a job, not reconcile or anything. However, it's not as easy as saying no. Once he does, everyone starts to fight him on it. He hesitates here, because his natural instinct would be to cave to the pressure and just do it so people won't be mad at him. In this case, however, his disappointment in Gendo outweighs all that. (This is only one of many, many ways where Shinji's life parallels my own...)