To be honest, I've always had a bit of dislike of NGE, and its mostly because every character is messed up and hard to like. Even the ones the fans do like (I really find the creepy attraction to the obviously emotionally damaged doll-like Rei in the fandom really really disturbing).
I've come to like it more as I grew out of my teen years, because of the things it does do well (though I still think it has major flaws), and through it all... I think Shinji might be the character I ended up liking the most. His reactions are really really understandable, even if they are "whiny". He is literally put in a position where nothing stands between the destruction of everything other than himself, piloting a "robot" that literally causes him to go berserk, he has no training for it, there seems to be zero counseling for him, and he doesn't have a real choice. There is no choice in his actions. Its do it or everyone ever dies. And he is 14!
At least he is honest about his completely understandable depression.