An interesting argument, and I do agree that western "civilisation" is in and of itself unsustainable. It's demise is inevitable. However, as other commenters have stated, you leave out the wars that will inevitably ensue. I believe the human race, left to its own devices, will use this crisis to create oppressive dictatorships and start wars (possibly nuclear). And, as a Christian, I believe that is why God ultimately steps in, so we don't destroy ourselves.