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The argument from fallacy, also known as argumentum ad logicam or fallacy fallacy, is a logical fallacy which assumes that because an argument is fallacious then its conclusion must be false.
Perhaps the simplest way to prove to yourself that this is a fallacy is think of an obvious truthhood and try to construct a fallacious argument in favor of it.
For example:
Now, even if you could disprove that angels will exert downward pressure on your pencil, it would not follow that if you let go of the pencil then it would not fall to the ground. It just means that "angel theory" is not a sound way of reaching that conclusion, regardless of the conclusion's truth or falsity.
Other Examples:
Showing that arguments given for a position are fallacies does not disprove the position. It may, nevertheless, be correct; the argument merely should not compel anyone to believe, either way.