It's very easy for us Americans to sit before our computers (that most people in the world could never afford), and presume "our" definition of "sane" applies perfectly to everyone else in the world. The fact is, it doesn't. the MAD concept works between us and Russia and China, because all these players understand MAD and want to avoid it. The concept accepts that if my cities are destroyed, yours are too. Since this is unacceptable to both sides, no launch occurs.
But if you're dealing with a fanatic(s) who "accepts" the destruction of his own cities/people as the "Will of God" or whatever his fanaticism dictates, the MAD concept falls flat on it's face. It ceases to work.
It wouldn't even require a fanatic necessarily, just mistaken belief. I remember when 9/11 occurred. Many of the people around me and even those in the news were speculating that the United States was teetering on the verge of collapse, as a result of panic. This was a ridiculous idea. The collapse of two buildings (albeit important ones) could not possibly trigger the collapse of the whole country. But plenty of American-born and bred Americans sincerely, honestly, believed America would fall into barbarism over the event. If Americans, who should know better, believed this, what of some fanatical Khomeini or Asian dilettante? They already perceive us as fat and morally weak. Perhaps they might also believe that the loss of one entire city could cause complete disarray, spasms of panic, followed by immediate collapse with no retribution at all. They might actually believe they could get away with it. We on these boards, know this is stupid, but who is to say that someone who sees us as moral defectives will have the same understanding?
ABMs such as the SM-3, are there to guard against failures of MAD for whatever reason. The US and Russia understand each other well enough, so such systems are not designed with Russia in mind. They're designed for those who cannot understand, or refuse to understand, or are simply ignorant of why MAD has protected us all for so long.