It is common to hear Christians argue against atheism on the grounds that it is impossible to prove a negative such as “God does not exist.” Only an omniscient being could do so, but an omniscient being would be God by definition! This sounds convincing, and has great rhetorical value, but it is a bad argument nonetheless.
There are a couple of glaring shortcomings. First, it is a straw-man. Most atheists do not claim to know with certainty that God does not exist. They only claim that His existence is very unlikely, or vastly improbable.
Secondly, the atheist could offer a similar argument against theism. One cannot know God exists with absolute certainty. While there may be very good grounds for thinking God exists, such knowledge is not certain. We could be mistaken (meaning it is not logically impossible for us to be wrong in this belief). In fact, virtually everything we claim to know, we know on probabilistic grounds, and yet we are justified in claiming to know it. If it would be unfair for the atheist to claim theists cannot claim to know God exists unless they have proven it impossible for God not to exist, then it is also unfair for the theist to discount atheism on the grounds that no one can be certain God does not exist. If there are good reasons for thinking His existence is unlikely, then one is justified in claiming to know God does not exist, even if they cannot be certain of this knowledge.
When you think about it, all of us claim to know certain things do not exist (unicorns, leprechauns, Santa Clause, the Greek gods, etc.) without being omniscient, and without proving their existence logically impossible. But are we certain of this? After all, we are making a claim about a negative, and it is impossible to prove a negative. The fact of the matter is that we cannot be certain that unicorns do not exist. They may exist on another planet or in another dimension that we are not aware of, and yet, given the lack of evidence for their existence we are justified in claiming to know they do not exist, even if we could be mistaken. Likewise, atheists are justified in claiming to know God does not exist, even if they cannot be certain of His non-existence. That’s not to say I think they are right, but it is to say their knowledge claim is not an illegitimate one simply because it lacks certitude. If certitude is the criterion for knowledge claims, it would make skeptics of us all.