There is one argument above all others in which I do not enjoy, and do not support in New Atheism and general atheistic arguments, and that is "You can't prove a negative" and the "Burden of Proof" argument, and I cannot find a single instance in which this works except when someone who is not making a negative claim. Here's why.
Alright, so let's say there's a man who walks up to you and says that he can do fifty cartwheels in five seconds. I tell him I don't believe him. He's going to have to prove such a thing. It is obviously not the skeptics burden of proof. This is all well and good. Now, let's say that there's a man who is in protest of such a thing, and starts saying, "There is no way for this man to do such a thing." Well, that's a claim, right? Well the man starts using the burden of proof argument. Except, this is not a claim to skepticism, this is a claim in itself, and he has just admitted that he can't prove a negative. Why in the hell would he make the claim then, if he can't prove it? To make this clearer, I'll give an instance of the burden of proof in other areas:
In claims in science, whether it's a negative or not, the man who is making a claim will have to provide the evidence, either for or against it. If it is a positive claim, they will have to give the evidence for it. If it is a negative claim, they will have to give the evidence against it. Now, I understand that in most areas, it is impossible for one to prove something doesn't exist. Still, that brings me back to my point: why make the claim? I feel it's completely unfair to say that one side has to prove something, and the other doesn't. If a side makes a claim, whether something exists or not, it seems entirely more fair to own up to that claim instead of galloping around thinking that you can say whatever you want because its a negatively claim, and again. I understand if it's a claim to skepticism, because then, obviously, it's not their burden of proof, but when someone is going to make a claim of a non-existence of something, it's better to give the arguments against that, instead of giving a cop-out.
And that is why I feel it's better to stick to the claims like "There is no evidence for God," or, "God is not essential to the runnings of space-time" because these are claims that in a way can be backed up with evidence. But to claim that a God doesn't exist, and then cop-out and say that the burden of proof is on you? That is entirely unfair, whether it's a negative claim or not.