I think that this point was addressed adequately at an earlier point in the thread. Who judges whether the burden of proof has been met? The atheist or the theist? In order for the argument to carry any persuasive force at all, you have to get the theist to agree. The strategy is supposed to get the theist to start presenting evidence to refute it, but the more typical response is "You're nuts!" OTOH, if you approach it as an argument over whether belief in gods is a reasonable belief to have, you might actually get a discussion. We aren't talking about a scientific or mathematical "proof" here. We are really talking about how one makes sense of nature and reality.
Quite true. It's just that most believers believe that they have sufficient proof of the existence of God (or some other gods), even if they can't make you see it. Are they being unreasonable?
Let me put it this way. Physicist
Brian Greene believes that string theory has a reasonably good chance of being true. It isn't a religious faith or dogma, but he thinks it worth committing a considerable portion of his life to that idea. The thing about string theory is that we don't really know whether it a testable idea. The math is compatible with it, but we cannot yet falsify it. So his belief is grounded in little more than intuition--kind of the same thing as religious belief in God (although I wouldn't go so far as to equate it with a religious belief, given that he willingly accepts a "burden of proof" debt). Maybe he isn't being entirely rational about it. I know that very intelligent people can go to extreme lengths to justify their biases. Ultimately, though, one has to admit that his bias is at least reasonable. I believe that a great many theists are similarly committed to their faith in a god--that it is a reasonable belief to hold. Do they need to prove it to skeptics? Maybe ultimately they do, but they still think it a reasonable enough belief to go on believing it for the time being. Not all theists are fanatics, but are they right to maintain that their belief is reasonable? Is it, as Dawkins has argued, a fairly obvious delusion? That's the real question, not whether they can prove the existence of God.