The idea that Asuka is 'the right match' for Shinji. Of course, this is all IMO.
Anyways, as I see it, Shinji as a character responds better to affection than he does aggression. He's spent his whole life starved of it, having been abandoned by his father, and we see that he will gladly receive even the smallest act of affection. The fact that just two words of approval from his father after a mission are enough to (temporarily) validate his father in his eyes shows how affectionately starved the poor kid is.
More importantly, if I remember right, it's only when Shinji is treated with affection that he is able to deal with the situations he is faced with. Remember, it was not his father's initial letter that brought him to Tokyo 3, a letter we see ripped up, but Misato's photo. When Shinji ran away from Tokyo-3, it was because of a lack of affection. It was only Misato, the only character to have treated him with any warmth, who was able to bring him back. Conversely, when Misato goes through her own personal crisis and withdraws that affection, we see that Shinji ultimately withdraws himself as an individual. He becomes unable to cope with the weight of being an Evangelion pilot and the associated horrors, such as Rei's death.
As much as Asuka lashes out at Shinji, we have to ask, is that really good for him. In any other case, I would agree that a lack of 'mollycoddling' wouldn't do him any harm. But that is precisely Shinji's problem: he has spent his whole life without any form of mollycoddling. His issue is that he's already been forced to live an independent life without any strong parent figure. We can see in the show that he's already learnt how to cook for himself and look after himself. It's implied that he's doing most of the running of the flat, what with doing most of the chores and Misato constantly being passed out drunk. Shinji is a kid who has had to make do without the support and love that most kids get to receive, and in that instance I'm not so sure that a large dose of Asuka would be all that good for him. His growth as a character is tied to how much affection he is given, and Asuka is simply not the type to give that affection readily. If Shinji were a regular boy, then she would be a great way to show him that life can be full of trials and obstacles, but Shinji isn't a regular boy, and his problem is exactly the opposite: he knows life is full of obstacles, but he needs someone to show that it can be full of warmth and love too. Hence why, I would say, in thematic terms Misato is the most important female to him, even if the implications are squicky squicky squicky.
As you can probably tell, I'm not the biggest fan of Asuka. As a piece in a larger narrative, she's absolutely fine, and is a great reflection of many of the shows themes and ideas, but as an actual person I just cannot like her, even if she did have a somewhat traumatic past.
