Topic on Talk:Cool Motive, Still A Crime
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Usually a Complete Monster has no excuse whatsoever. A Freudian Excuse makes a villain at least slightly tragic, and thus disqualifies him from a Complete Monster label.
Of course, with many Freudian Excuse cases, the background can be subjected to the villain's biased view of the facts. For example, Fantastic Four villain the Mole Man claims he had a Friendless Background where he was antagonized for his ugliness, but then, The Official Handbook of the Marvel Universe points out that every story about his past has been related by the Mole Man himself, and thus could well be tainted by his own biased interpretation. Unlike, say, Dr. Doom, a villain whose tragic past can be confirmed by more trustworthy witnesses.