Fallacy (noun)

1. A mistaken belief, especially one based on unsound arguments.
2. A false or mistaken idea.

Origin:

From the latin fallacia, meaning "deception".

Examples:

1. The argument was based on a common fallacy that correlation implies causation.
2. The politician's statement was a fallacy and easily disproved by the facts.
3. The advertisement contained several fallacies, including a false dilemma and an appeal to emotion.
4. The fallacy in the argument was pointed out by the opposing team.
5. The belief that the earth is flat is a fallacy that has been disproven by scientific evidence.