There's a corollary to this argument against atheists who say they only use reason when they don't:
If you can't tell the difference between what you say is true and what actually is true, you aren't reasoning very well.
So why exactly should I accept your reasoning?
And perhaps this can be taken a step further. The only one for whom there is in fact no distinction between what they say is true and what actually is true, is God. What God says, is.
So here we have an atheist who, in arguing that there is no God, acts like God. And not just any god, but the God of Abraham.
There are a lot of possible explanations for this. That the omnipresence of God extends even into human arguments against His existence is just one of them, but it may be the most satisfying.