All or nothing fallacy:

Definition Example
When it is suggested or implied that one must believe all or nothing of a particular set of beliefs. Saint Nicholas clearly existed, so why are you suggesting he does not descend chimneys in a red suit Christmas eve?
Most famous individuals throughout history have some degree of mythology attached to their lives. This fallacy is related to the false dilemma fallacy and the piggy-back assumption fallacy.

Case Study One

Some Christians cite evidence that some of the historical references in the Bible are collaborated with extra-biblical sources, then imply that everything found within the Bible, including the miracles, are also true.

Case Study Two

Some atheists confront theists with arguments against the notion of Hell, though many theists do not believe in an actual burning Hell, claiming that biblical references to Hell are merely allegorical.

Keep in mind that a fallacious argument does not entail an erroneous position.

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