He was home schooled. They kicked him of public school because of his anti-social behavior.
Again, he was 20 years old, and presumably had finished high school. He did attend high school, or else they couldn't have interviewed one of his teachers. Now, his teacher says he was a nerdy kid who wasn't the "bully" type, but more the type who might be bullied. He didn't indicate Adam was "anti-social" he just said it seemed he was a little withdrawn or reclusive.
But "anti-social" is not "mentally ill" and doesn't mean he was being treated for mental disorders. Your argument, again, was that we should not allow weapons in homes where there is a mentally ill person, and I agree... but there is no evidence Adam Lanza had been diagnosed as mentally ill or was being treated for mental illness. So your argument has a problem, and now you run to "well he was anti-social!" Okay, so you want to ban guns in the homes of anyone who is anti-social? Well, how about banning guns in the homes of anyone who's parents are divorced? How about just anyone who is a little odd or strange? And who gets to make this determination? OH WAIT.... let me guess-- Government?
Let's be clear, we OBVIOUSLY know now, that Adam Lanza was a very disturbed young man, that's not hard to figure out. I see nothing about him that would have indicated he was going to do something like this. Millions of kids fit his profile, millions of them can get access to firearms. In order for your "no guns in the house with the mentally disturbed" idea to work, we first have to put in place a reasonable way for their parents and family to have them deemed mentally disturbed. Currently, we have just the opposite, we have a system where it's virtually impossible to have someone committed for evaluation. The stories out of CT are that his mother was actively pursuing these avenues, and was planning to have him committed, and that's why he snapped. I can't help but think, if it were as easy as it once was, maybe Adam would have been in an institution already?