I can't remember saying anything about sterilization explicitly. What is needed before anything else is attempted, is a change of societal values.
Values have already changed a lot. There was a link to a presentation by Pinker in the "government and happiness" thread which is worthwhile. He basically says that we've come a long way since the middle ages and before that, in terms of reduced cruelty anyway. I'm quite confident myself that sensibilities are going to develop even further in that direction.
However it is sad that social groups don't like to behave in a way that's associated with the upper classes for fear of rejection by their peers. I think it's explainable from a psychological perspective but there's nothing reasonable about such an attitude IMO. So you're right in that the class system doesn't do any such thing help. But, to what extent is the class system a construct? I don't think there's an easy way to tell.
To some extent it may be a construct, but then again it's not. You're right, it is difficult to tell. It can't be dismissed entirely as a construct, though. Wealth, class culture, different typical attitudes, all these exist and are transmitted to children from parents and peers. Certainly you can't define someone as, e.g. working-class to be the be-all and end-all of what they are. Upward mobility (downward is rarer) is possible to a degree, but very difficult for somebody with a really nasty background, in view of the possible factors which can hold him/her back, one of these being that he/she doesn't have the right - hell, there's a German word for it, "Stallgeruch" - "stable smell", the English escapes me right now - well, when he/she doesn't show the right airs and manners and upbringing, for example when applying for a job.
My only quarrel with eroding any class system is that it always ends up getting taken too far, an egalitarian perspective is not a good one. For example since they tried to cram as many people as possible into universities I've noticed a higher proportion of people who clearly aren't suited to an academic environment at all and clearly don't enjoy that side of it. Some people aren't cut out for academia.
I am a convinced egalitarian, in several senses actually. Firstly, I believe that everyone should be equal before the law. I don't know if you agree here, but I sure hope you do. Then in a not so trivial sense, I recognize that every life is worth the same, be it the life of an asshole or of a saint. I'm sure many on this board cannot follow me there, still it's a conviction that I hold.
In an even less trivial sense, I think that everyone deserves a good shot at using their potential. Obviously we're not all gifted in the same degree, but I think that everyone should have the possibility to realize their potential, and that if extraneous factors stand in the way, society should mitigate them or, if possible, remove them. That is why I am for free tuition. Any move to get more people to access the university system is fine with me. Some people may indeed not be cut out for academia as regards the necessary intelligence or will to work - they'll drop out. But that they don't appear to harmonize with the environment, if I may paraphrase thus what I understood you to mean, and therefore don't belong there, is a really strong prejudice on your part, if that is what you wanted to express. A university is basically a facility, after all, and its primary purpose is not to supply a venue for a social gathering.
What is the problem with eroding the class system, or better, what is the point in keeping it? What is the point in keeping privilege by birthright? If the upper class appears to do better in the jobs they hold, in the money they make, in the behavior they display (apart from unwarranted arrogance), it is - in my belief - because they had better chances to start with, more money to go into their education, the right "stable smell", a surrounding that saw to it that they hold knife and fork in the correct hand and don't set fire to ambulances. It's not because they're inherently superior. And, more importantly, what's the point of keeping people underprivileged? I don't see one. It's a great waste of potential resources, societally speaking, and damn unfair, personally speaking.
As to how to combat the shitty behavior sometimes seen in the shitty parts of town, it's difficult. I don't know of a patent medicine. I point again to Pinker's talk, which leaves me mildly optimistic. I do believe, though, that there is a correlation between feeling frustrated and disenfranchised and "What the hell" behavior, in the sense that if the world doesn't care about me, I won't care about the world. This tends to get worse the stronger the feeling of being underprivileged and really having not much of good future ahead of you gets. (I know it can be used as an excuse too, but I don't think that does quite invalidate my point.) As I said, I believe that the level of uneducated barbarism was actually never lower than today.
Maybe education is the key. From the top of my head, maybe a scheme to pick out the quiet ones, the bullied ones from the shit schools and giving them the chance to go to a better school could be an idea. That, however would presuppose that they're not looked down on at their new school, something that I'm sure will happen quite a lot. A class border always has two sides - don't forget the ones who are prepared to look down on someone, they may do their share in perpetuating the system and its problems.
I'm sorry, that was a long-ass rant, and not all of it was concise debating or swaying arguments. Some questions, however, cannot be conclusively answered by earnest pondering of all contingent factors; it often comes down to taste and opinion in the end, and well, for what it's worth, there you have mine.