First of all I would like to say that in each "school killing" incident I try to understand if it falls in a category, for example the shooting by Pekka-Eric Auvinen can be a pure example of the "desperate smart kid" category, a shooting because of a girl is another category and a shooting like that Batman/Joker shit that happened recently in the US, which really made me laugh my ass off, is pure surrealism. Of course, there can always be overlaps Let me explain:
Imagine that there is a smart kid, John. John will show potential in his very first years, learning stuff easily etc. Before adolescence I believe these kids generally show potential, before they are ushered in more heavy sexual/societal pressures which are handled impossibly wrong by our enlightened modern society. If you think porn, promiscuity, pressure to have trendy opinions, dress trendy, speak with ebonics or whatever is "in" in your country, you are getting my point. So let's assume John also has some X degree of social awkwardness. It is highly probable that he will not fit in as much as is needed to be happy. Probably he will be bullied because of this. He will not have a girlfriend, will have limeted to no sexual experience, expotentially his sexual frustration will grow so will his alienation and finally so will his frustration. Frustration (in my opinion) tends to manifest it self through desperation and/or anger. If John's character is such that he blames himself he will tend towards escaping to the void, if it is such that he blames "the others" he will tend to hate them, and of course if you hate some people, if you go postal you might want to erase them from the face of the earth. (From what I see Adam Lanza interpreted what I called "the others" as this school, but I am talking in general here, for the hypothetical John).
So it all boils down to what that X Degree of social awkwardness was and by what it was caused. Let's take two extremes and the middle. If it was extremely high and it was innate, he would have probably not fitted into any society and although this society is the perfect one to make him a pariah and drive him insane I would have to acknowledge that his genes/early nurturing might had made him let's say a 'negative' person (someone might disagree since the greatest development and brain rewiring happens in adolescence but whatever)
The other extreme, if he had extremely low X degree of social awkwardness it is fairly clear that external pressures and this alien society made him feel like trash.
I believe most cases fall somewhere in the middle, smart kids with low social skills which find themselves isolated because of perceived 'weirdness' which in the criteria of stupid, crude, social chameleons and other human trash might be just because he doesn't talk trendy or hit on girls with the ratio of the 'alpha males' (some develop sexuality later than others, and by the time they do are already pariahs because they didn't develop it earlier). These 'middle' kids would have fit better in another, more sane society with better values. Low social skills doesn't immediately mean absolute isolation, or let's say shouldn't. In fact I have many friends who during adolescence were just... not loud, for fuck's sake men, and were treated like garbage by bullies, some were still virgins up to their early twenties. I swear that I am not judging lightly, I am not talking about aspies or ugly weirdos etc.
That's all I have to say, and remember I am talking about generally about 'desperate kids who had potential', not specifically about Adam Lanza. I think my post is also an answer to Harry Potter's question.