Atheists... why do you believe that God doesn't exist?

[Rampant.A.I.]

It's amazing to watch the kind of intellectual gymnastics people will go through rationalizing why they don't need to support their claims.

When debating any issue, there is an implicit burden of proof on the person asserting a claim. An argument from ignorance occurs when either a proposition is assumed to be true because it has not yet been proven false or a proposition is assumed to be false because it has not yet been proven true.[1][2] This has the effect of shifting the burden of proof to the person criticizing the assertion, but is not valid reasoning.[3]

No one is saying the conclusion is assumed to be false because it has not been proven. They are saying they reject your claim in the absence of proof: Note the loudest protestors that their claim is true cannot provide a logical argument for why, they can only advance more claims that it is valid.

http://en.m.wikipedia.org/wiki/Philosoph...n_of_proof

burden of proof
You said that the burden of proof lies not with the person making the claim, but with someone else to disprove.
The burden of proof lies with someone who is making a claim, and is not upon anyone else to disprove.

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The inability, or disinclination, to disprove a claim does not render that claim valid, nor give it any credence whatsoever. However it is important to note that we can never be certain of anything, and so we must assign value to any claim based on the available evidence, and to dismiss something on the basis that it hasn't been proven beyond all doubt is also fallacious reasoning.

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Example: Bertrand declares that a teapot is, at this very moment, in orbit around the Sun between the Earth and Mars, and that because no one can prove him wrong, his claim is therefore a valid one.

https://yourlogicalfallacyis.com/burden-of-proof