This argument informally states that no particular theology or version of God is believable, since arguments for the existence of God apply generically to many religions.
The argument for the existence of God known as Pascal's Wager states that nonbelievers should change their minds even if only because of precautionary reasons. One common reply is that given the proliferation of different religions, it is extremely unlikely that any one will bet on the right God. This is one instance of the argument from inconsistent revelations at work. There's an enormous variety of religions and denominations within them, many of whose claims are logically incompatible with one another. The argument from inconsistent revelations does not intend to be a deductive syllogism for the nonexistence of God, but rather a probabilistic argument. From the existence of multiple incompatible faiths it can be argued that probably no deities exist (or that they do not care for humanity). Otherwise it would imply that they have miserably failed at establishing a clearly epistemologically superior religious tradition.