Here's the way I see it. It's been forever since I watched it, so some of this might be way off.
Evangelion attracts a lot of fanboys because it has nice looking giant robots. The story has almost nothing to do with the robots, but most people just don't understand this because the robots are front and center the whole time.
The show is about a big pile of really fucked up people with a lot of money and a lot of military power. They spend most of the time being totally insane, some more than others. Gendo's motivation is to become God, for instance, and is willing to sacrifice everything and use everyone to do so.
Shinji has it tough, considering all the badmouthing he gets. His mom is a giant robot, and his dad doesn't give two shits about him, and in fact would rather put him in life threatening situations just to further his goal.
Asuka, his closest acquaintance of his age, is clinically depressed because she feels responsible for killing her mother, and is overcompensating for her HUGE level of insecurity by taking it out on Shinji. She validates her existence by excelling at controlling her eva unit. When Shinji schools her at that, she shatters like glass, and takes it out on him some more, before receding into a little made up reality of hers to escape the shame and pain.
She has a chance to make good on it when Shinji is breaking down towards the end, and needs support, but decides to be a gigantic bitch instead in an attempt to salvage what little pride she has left, and he chokes the shit out of her and puts her into a coma. Good.
Then he jerks off on her like the trashy slut she is.