A false dilemma is a type of informal fallacy in which something is falsely claimed to be an "either/or" situation, when in fact there is at least one additional option. (from wiki)
The dilemma presented is usually like this:
'If you cannot prove God's existence, then He does not exist!'
But, there are other possibilities, not just the 'either/or' of this dilemma.
1. God may have reasons, unknown to us, for not presenting a conspicuous presence.
2. God may reveal to some, but leave others wondering.
3. The Majesty and holiness of God may be too much for sinful man to observe, so God waits, to give opportunity to be reconciled.
4. Something has blinded the awareness of humans, so they are unable to grasp the obvious.
5. God does not reveal Himself, because He does not exist.
We do not have enough evidence, individually, to categorically declare one of these possibilities as 'truth!', and dismiss all others. Therefore, this argument is fallacious, based on a false dilemma.
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