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Fallacy (faith)
Narcissists argue in what is sometimes referred to as bad faith. It means that they don't even care about, or try to understand, the other person. Or even worse, they are dedicated to deliberately misunderstanding and mischaracterizing others, often to the point of absurdity.
They are willingly dishonest, deceptive, and morally corrupt. Often while at the same time quick to accuse others of being dishonest, deceptive, and morally corrupt.