Occasionally I encounter materialist atheists who demand physical proof for the existence of God. Such demands are what is known as a categorical error. Science belongs to the category of the natural... that which can be observed and studied and tested. The category of the natural involves the entire physical universe.
The problem is, if something has existence in a way that goes beyond physical existence -- what we call supernatural -- then trying to apply the principles of the natural universe to studying the supernatural is using a tool which is entirely unsuited for the task. It would be like using a microscope to try to study the stars.
Atheists of this type make some underlying assumptions that they do not question. But the problem is, they make arguments using these assumptions but the underlying assumptions need to be proven before their questions can be considered justified.
Some of the assumptions are:
1) The supernatural does not exist
2) If God exists there must be physical evidence for that existence.
3) Belief in the supernatural comes from pre scientific superstition
4) Science has eliminated the need to believe in God
Others exist, but these are some of the basic ones.
The problem is, when the atheist demands physical proof of God's existence, they are effectively making a universal negative claim about reality. The onus of proof is on them for making that claim, but being a universal negative, it is impossible to prove.
This is where you get ridiculous statements like "the burden of proof is on the person making the more extraordinary claim," or "since you can't prove a negative, the burden of proof is on the person making the positive claim."
It is always the person making an argument who has the burden of proof, so the atheist making these statements is guilty of shifting the burden of proof. He or she makes an assertion and then, instead of proving it, demands it be disproved.
Such a tactic tends to be used on the Internet against believers who the atheist believes is not skilled in argument. When that particular believer lacks the skills to refute the challenge, the atheist then declares victory for "disproving" Christianity.
But he hasn't. Refuting a weak opponent doesn't automatically mean the case for Christianity is weak. It could just means the weak opponent does not know his faith well enough to understand a complex philosophical attack against it.
Conclusion
Once you can see the big picture, you can see this kind of attack is unquestioned assumptions that need to be proven combined with shoddy tactics used to confuse and intimidate the opponent and make observers think the atheist has proven a point he has not proven.
Unfortunately, the Internet being what it is, attention spans are short. Usually the best you can do is make your case -- politely -- in the hopes of reaching people of good will and encouraging them to consider what the truth is.
As an afterwards, I'd like to point out that not all atheists use these dishonest tactics. Nor is it limited to atheism. I've seen fundamentalist anti Catholics behave similarly, as well as radical traditionalists bash other Catholics.
The basic flaws in all cases are:
1) unquestioned assumptions used as a basis even though the opponents believe it to be false.
2) attempts to shift burden of proof
3) tries to make defeat of unskilled opponents into refutation of position.
The basic counters are:
1) don't let the false assumption go unquestioned.
2) don't let the opponent shift the burden of proof onto you when he made the assertion
3) study what you believe so as not to be an unskilled opponent.