When an atheist demands a theist provide evidence for God’s existence, one of two dynamics is in play.
First, the atheist could be someone who sincerely believes that all claims must be supported by evidence. As such, this person is standing on principle and their demand simply follows from this principle.
Second, the atheist could be an apologist or activist who is trying to posture in way where they occupy a position of judgment and authority. As such, this person is engaged in a tactic designed to serve the ends of his/her agenda. What they are trying to do is set up some sort of kangaroo court proceedings to serve their own personal needs or the needs of the Gnu atheist movement.
So how can you, as a theist, tell what you are dealing with? For what reasonable person would want to waste time and energy subjecting themselves to some needless kangaroo court-like exchanges?
There are two simple questions that can be asked before any attempt to satisfy some atheist’s demands.
1. Ask the atheist to provide the evidence that they can consider the question/demand in an open-minded and fair-minded manner. This is a most reasonable request. If you are to take the demand as a sincere expression of curiosity and principle, you don’t want to find yourself being misled into some maze-like kangaroo court. Now, if the atheist is someone who sincerely believes that all claims must be supported by evidence, they will be happy and eager to supply evidence of their open- and fair-minded approach. That follows from them standing on their principles.
If, on the other hand, the demand is a disingenuous trick designed to bait you into some kangagnu court, the atheist will a) ignore the request; b) be insulted by the request; or c) come up with some excuse or rationalization for not having to satisfy this request.
2. Ask the atheist what they would count as evidence for God’s existence. If the atheist is trying to posture in way where they occupy a position of judgment and authority, they will refuse to make any attempt to answer the question. If the atheist wants to posture as some Judge in the Kangagnu Court, he/she will be invested in hiding the goalposts. By hiding the goalposts, the atheist can ensure the court is rigged to always reach the judgment the atheist seeks.