What the Fallacy?!
Burden of Proof
The Fallacy
Saying that the burden of proof lies not with the person making the claim, but with someone else to disprove.
Why it's wrong
The burden of proof lies with someone who is making a claim, and is not upon anyone else to disprove. The inability, or disinclination, to disprove a claim does not render that claim valid, nor give it any credence whatsoever.
Example
Kevin claimed that there is a microscopic civilization living on his left pinky finger. When asked for proof, he insisted that since no one could prove they *weren't* there, they must exist.