When they casually drop the mask and betray their target's trust, their secret insidious natures are never revealed to anyone else. Unsuspecting bystanders always like to give others the benefit of the doubt, so any witnesses think that the psychopath's intentional wrongdoing was merely an accident. The victim is not believed because the sheep costume is all the others see. The line of surprised victims grows unchecked.
When the Wolfsheep coldly reveals its total deception, the prey has a visible emotional reaction; rage, depression, misery, shock, and may attempt to get revenge. Too bad all the other unenlightened friends defend the Wolfsheep's apparent "innocence". What harm did the Wolfsheep do? No pain on earth comes close to having completely believed in, and trusted your life to, the mild-mannered Wolfsheep, only to later discover the true face of it's uncaring unfeeling untrustworthiness.
How does the Wolf in Sheep's Clothing get away with deceiving everyone, and getting their complicity against the prey? Firstly, no one double checks both sides of the story. Secondly, the Wolfsheep has been priming them all with lots of expert storytelling, building his/her believability. Anyone who checks the facts of any of the stories learns the truth, confronts the Wolfsheep, explodes in outrage at the lengthy timeline of having been duped by someone they practically worshipped, and gets to be the next victim. More details on the psychopathic M.O. in the FAQ.
After spending it's whole life in sheep's clothing, can the wolf become a sheep on the inside? No, it doesn't even try. It's too much fun getting people to believe the costume.