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The burden of proof lies with someone who is making a claim -- not with anyone else to disprove. Russell argued there was a teapot in orbit around the sun somewhere between the earth and mars. He then placed the burden of proof on anyone who wished to disprove his claim. In doing so, he was committing a logical fallacy.
But Russell was a preeminent mathematician and logician. So, some people have argued, that Russell intentionally misplaced the burden of proof in order to ironically illustrate his real point. His real point being that those who claim there is or might be a god because you cannot prove there isn't a god have misplaced the burden of proof. That is, they have committed the same error that Russell (presumably intentionally) commits with his teapot argument.