The Problem with Natural Theology

I want to expand a bit on a concept I talked about a while back in my post on ontological naturalism: namely, the idea that supernatural concepts are fundamentally incoherent. Theologians argue that theology is, like science, a viable means attaining knowledge; I am going to argue that theology is in principle incapable of imparting us with knowledge.  I'm not concerned with theological debates over doctrine (revealed theology), but rather natural theology. From Wikipedia:

Natural theology is a branch of theology based on reason and ordinary experience. Thus it is distinguished from revealed theology (or revealed religion) which is based on scripture and religious experiences of various kinds.

Natural theology is what most apologists, from C.S. Lewis to William Lane Craig to Francis Collins to Alister McGrath, are preoccupied with; it's the idea that we can use our understanding of the natural world to make inferences about the existence and nature of divine or supernatural things. Take, for example, the Kalam Cosmological Argument:

1. Everything that begins to exist has a cause to its existence
2. The universe began to exist
3. Ergo, the universe has a cause to its existence

The purpose of this argument is to articulate what we feel is intuitively true – the idea that something can't come from nothing – and cantilever those intuitions into realms that are beyond our immediate, objective reach. In other words, it's attempting to use our intuitive understanding of the world around us to infer things about worlds beyond us. That's the crux of all natural theology and, as I aim to show, its downfall.