If you make a claim you need to be able to back it up. It may very well be the case than during a debate, someone says 'but God doesn't even exist' without anyone specifically claiming that He does. In this scenario it is not up to everyone else to prove the guy wrong; he's the only one who actually made a claim about God, so he's the only one who has to prove anything. As far as the other guys are concerned they could have just been expressing opinions rather than intended truths.
It isn't for the other people to prove him wrong, that's exactly the same argument people who claim God exist use and you'd call that fallacious, so don't be a hypocrite.
If you can't prove 'God doesn't exist' then don't claim it in a debate scenario. Simple as. If you have to say something then state your opinion because you don't need to prove your opinion.
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When did I say anything about proving "God doesn't exist?" Red herring is also a logical fallacy. Keep that in mind.
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I never said you said that; I was using it as an example of how the burden of proof isn't solely on the person claiming the positive statement.