A thought just struck me: we have no idea how Nancy really behaved when it was just her and Adam. Thus the question "why did Adam kill his mother?" becomes even more unanswerable. Maybe she was sweet as pie, trying to comfort him only to be rebuffed. OR, maybe she was mean to him, either explicitly or implicitly, implying that he was a liability or showing a general lack of affection. Reports from Peter Lanza and her friends suggest otherwise, but we can really never know when we don't have a direct account from either of them, which would probably be unreliable anyway. Plus, as C. W. Wade has pointed out, it's likely she was a alcoholic; there was a lot of wine in that house, and we know Adam didn't drink.
Just an interesting thing to think about.