Religion tries to prove God exists. Atheists try to prove God doesn't exist. Both sides make arguments for their side that are compelling. Religion states just because you can't scientifically sense God doesn't mean an almighty being isn't out there, it's just that being hasn't been scientifically proven yet. Atheists make the opposite case--God does not exist because that being isn't in a tangible form. Both sides of the unending argument will go back and forth in perpetuity.
It answers this question admirably. There could be a china teapot orbiting the sun in between Earth and Mars that has not as yet been discovered, but no sane person believes there is. If someone wants to convince me of any assertion, they need to be able to prove it, or at least provide compelling evidence.
Atheism doesn't make any claim its merely disbelief in god and religious texts. Atheism also listens to what science has to say and what is proven. Religion does not it claims god exists so the burden of proof is on religion not atheism. That is because it claims a hypothesis is true without sufficient evidance to back it up.
Atheism is not the position that no god exists, which would have a burden of proof. Atheism is the position of being unconvinced that any god exists. The difference is subtle, but the key issue here is that someone who does not find any theistic claims convincing or rationally justified is by any reasonable definition an atheist, even if that person never professes the non-existence of any god.
In terms of logic and argumentation, the burden of proof always rest with the person making the claim. The postion of atheism doesn't make a claim it is just the postion of the person not agreeing with theistic claims. So what burden of proof does the atheist have? In our court system the burden of proof always rest with the prosecution, they have to prove their case beyond a reasonable doubt, if they fail to do so, then the judgement is awarded to the defendent. It is not the defendents responsibilty to make the case it is the plaintiff/prosecutor, it is only the defendents job to defend it.