By your definition of madness, insanity is a lack of rationality and the inability to self-reflect. That's a fair enough definition, but I think it's different from what AtroposHeart is talking about. Atropos is talking about mental illness - an issue with a brain that is caused purely by biological circumstances rather than social ones. By your definition, I'd argue that madness could just as easily be a product of culture as it might be a matter of chemical imbalance. Irrationality and narcissism can be taught as well as inherited.
That being said, I'd like to reiterate my own point - I don't think you can argue that either mental illness or culture are solely to blame for this. Neither would have caused this to happen if the other wasn't in place first. Elliot was a product of his defective biology as well as his defective upbringing. He was a narcissist whose delusions regarding self importance were constantly confirmed by those around him. Had he simply been a narcissist living in a lower or middle class home, he would likely have expressed his delusions in another way, perhaps just as violent, perhaps not. If he'd simply been a spoiled kid who believed women were objects but lacked any signs of mental illnesses whatsoever, he would have likely continued disrespecting women who didn't enjoy his company, but his less-repressed ability to self-reflect might have helped him learn how to manipulate some poor woman into being with him for at least a night.
You can't make 2 with only a single 1.