Great answers from other posts especially about the recommendations to get better schooling and knowledge on logic, critical thinking, etc. This, arguably, is one of the key reasons the GB do not encourage (often discourage) higher-education. Here is another way to think about the position the atheist is taking:
In the US criminal justice system, a person is either declared "Guilty or Not Guilty". The burden of proof is on the prosecution. The jurors hear the prosecution's evidence and go away and bring back a "guilty" or "not guilty" decision. They are in fact voting on a two-pronged binary question - i.e. is the person guilty or not guilty. If the jurors come back with "guilty" it means that the prosecution met the "burden of proof". If the prosecution does not meet the "burden of proof", the person is declared "not guilty". However, and this is the important part, the jury is not voting on whether the person is "guilty" or "innocent". "Not guilty" is not the same a "innocent". Even if the person may have indeed committed the crime, all the jury can say with a "Not Guilty" vote is that the prosecution did not meet "the burden of proof".
So, if you wanted to use this as an analogy to the proposition "There is a God(s)":
- the theist is voting "Guilty" (the prosecution has met the burden of proof and to them "There is a God(s)")
- the atheist is saying "Not Guilty" (the prosecution has not met the burden of proof). However, this does not mean the same as "Innocent" ("There is no God(s)").
On a side note, this also shows why putting the "burden of proof" on the person making the claim is beneficial. In this legal system the "burden of proof" is on the prosecution (the State). If the burden of proof was on you (i.e. to prove yourself not-guilty) you could potentially be charged with all sorts of trivial/"made up" charges every day without good evidence (e.g. faith), be arrested every day, and spend all of your resources defending yourself, every day for the rest of your life. By making the prosecution have the burden of proof, it means that the State needs to use up their resources first before dragging you into the issue. And, the cost the State incurs become an incentive to decrease prosecutorial misconduct.
Likewise, I need not clutter up my brain and tax my resources on addressing every claim (e.g. God, fairies, conspiracy theories, chupacabra, etc.) until good evidence has been provided. I let the person making the claim spend their resources. It is not my job to make somebody else's case.