John is right. This is in the running for the dumbest theist argument ever.
The atheist might say, “Well, I can reason just fine, and I don’t believe in God.” But this is no different than the critic of air saying, “Well, I can breathe just fine, and I don’t believe in air.” This isn’t a rational response. Breathing requires air, not a profession of belief in air. Likewise, logical reasoning requires God, not a profession of belief in Him. Of course the atheist can reason; it’s because God has made his mind and given him access to the laws of logic—and that’s the point. It’s because God exists that reasoning is possible. The atheist can reason, but within his own worldview he cannot account for his ability to reason.
It’s from Answers in Genesis, so what else can you expect?