The show has this whole 'sexual coming of age' metaphor going on, based on the Freudian idea of the Oedipal stage where a boy competes with his father for the affection of his mother before he's able to move on and sexually relate to other girls.
Throughout the show Asuka is depicted as the 'other' who Shinji has difficulty relating to. She's the best representation of his inability to form connections with others, which the show talks about as being linked to the inability to truly see inside the head of one another (AT Fields and all that. Instrumentality was meant to be a way to get past this human 'limitation'). She's hyper aware of her sexuality and flaunts it to attract Shinji.
But remember, Shinji is shown to be a prude who tries to bury his sexual thoughts.
On the other hand, Rei is the opposite. Shinji can turn to her for comfort in the symbolic mind train sequences, and unlike Asuka, she never says anything that could hurt him. She's also completely unaware of her sexuality. Think about the awkwardness of the groping scene. In episode 14, it's implied that she may not even have a normal human reproductive system. So if Asuka is sex and differentness and the scariness of living a real life, Rei is the opposite. Easy comfort.
The whole idea of Rei as 'mother figure' is all over Eva. In addition to being a clone of Shinji's mother and constructed from the DNA of the great mother Lilith, she's the key to instrumentality, which is referred to as 'the return to the womb'.
Shinji starts instrumentality in EoE because he's afraid of Asuka (human contact and sex) and would rather run away to easy fantasy. It's the extension of that whole 'I mustn't run away' thing. Being inside a womb means that you are eternally comfortable, but you'll never move forward in life or achieve anything. That, as Eva hits us over the head with, can only be achieved through connections with other people, because we only have identities through our connections with others.
Shinji realizes this at the end, and leaves behind Rei's world, which is associated with familial comfort, fantasy and regression, and finds himself with Asuka, who is linked with the complex emotions of reality and with sex. There's a ton of 'childbirth' imagery here (Eva-01 emerging from a vagina, the blood spraying across the moon, Shinji's head emerging from red fluid) and at the end of the sequence Shinji says fairwell to Rei and Yui, and Eva-01 floats off to space. He has 'left his mother behind'.
Immediately after saying 'goodbye, mother', we cut to Shinji waking up with Asuka. In this scene, she's 'wearing' two bits of symbolism that were previously associated with Shinji's mother. She's wearing the bandages Rei wore the first time he saw her, except the sides they were on are now flipped. She also uses the caress that Yui used the first time Shinji sees her in the show (in episode 16) and as a farewell in the previous scene. In the context of the film, you get the idea that something has been transferred. After saying goodbye to his mother, Asuka, who is symbolic of reality and sex, has come to replace her role in his life.
So basically, they are going to fuck.
All of this works as an elaborate way for Anno to tell otaku to get out of their mother's basements and go and have relationships with real women. Funnily enough, he's said in interviews that people who prefer Rei to Asuka 'can't handle real women'.
Over the course of several years and finished in 1995, Neon Genesis Evangelion was made as a television production consisting of 26 episodes. After it's initial airing(s), the work proved to be immensely popular, reaching far beyond it's intended target audience - it was for instance not uncommon to overhear salarymen at bars discussing the plot and events of Evangelion.
This popularity sparked a movement that shaped today's otakudom. Akihabara transformed from a market centre for electronic appliances into the otaku haven it is today, and made possible the "late night anime TV-slot". It inspired an entire generation to start as animators, and as such, it's unmistakable influence is commonly found in many of the anime postdating it.
In short, the conclusion: NGE created the moe-business as we know it today. The momentum from the previously mentioned movement steered towards the situation we have today.
I believe it's likely that the moe-business is the result of Eva tramautizing a generation of viewers who completely failed to understand the implications of the series' message and thus retreated even deeper into otakudom. The plot so completely broke their minds with a truth they weren't willing to accept, that all they could say in response is "what the world really needs are endless derivative variations of Asuka and Rei doing cute things without all that emotional trauma making viewers uncomfortable."
Even now, Hideaki Anno is still making Evangelion. When he's done, who knows what will happen? What new risks and consequences will we face?
