The nature of evidence

[Angrboda]

No, that's your projection. Think of it in a courtroom situation - the only position held by the attorney for the defence is "the prosecution has not provided sufficient evidence against my client to meet the burden of proof". Sure, if Joe Blow didn't do it someone else must have,but that's neither the purview of the defence nor the issue under discussion.

Theists have a burden of proof, since they are the ones with something to prove. Atheists, in matters pertaining to atheism, do not.

I really can't make it any simpler without using crayons.

The burden of proof is on the one making the claim.   If you are claiming that something is false, then you have the burden to show the reasons/evidence for that claim.  I have run into a fair number of people who didn't understand this.  Atheist do have the burden of proof, as soon as they make any claim which is not agnostic.

The burden of proof is on the person making an existential claim. Other types of claims depend on what is being claimed, and where the dispute lies. Burden of proof is mainly a concept that is employed when someone wants to persuade or convince others of the truth of a claim. If the atheist is trying to convince you of something, regardless of burden of proof, it behooves them to support their assertion. Failure to do so simply means the attempt to convince the other may not be successful. However, as a theist, it's known that you believe in the existence of a god. Your failure to provide support for your belief when challenged is mere cowardice. Bark about burden of proof all you want, it will simply mark you as a prevaricator.