Consider, if you will, an argument for theism than which no worse can be conceived.
What would such an argument be like? Well, arguments that merely fail to provide any support whatever for their conclusions are two a penny; a worst conceivable argument for any proposition must surely be one that actually conclusively refutes the proposition it's meant to support.
Now, the worst conceivable argument for theism clearly exists in the understanding. But it cannot exist only there, for so bad an argument is of course worse (because more destructive) if it is actually made; so if it existed only in the understanding then a worse would be conceivable, which is a contradiction.
Therefore, there is an argument for theism which is in reality a conclusive refutation of theism.
But a belief that can be conclusively refuted is false. Therefore there is no God.
Note: Yes, of course the above is entirely ridiculous, and in particular I am of course not suggesting that it actually offers the slightest reason for rejecting theism.