CRAZY LIKE (OR AS) A FOX ? ??seemingly foolish but in fact extremely cunning.? From ?Random House Historical Dictionary of American Slang, Volume 1, A-G? by J.E. Lighter, Random House, New York, 1994. And from a second reference: Crazy (Dumb, Sly) Like a Fox. Smart and resourceful. The fox has been celebrated for centuries as a crafty animal. Its wiles were remarked in the ?Trinity College Homilies,? dating from about 1200. S. J. Perelman made one of the phrases (Crazy Like a Fox) the title of a book in 1944.? From the "Dictionary of Cliches" by James Rogers (Ballantine Books, New York, 1985).
If you say, "He's crazy like a fox," you are saying that person is smart and can outwit other people. The image I get is that the actions of a fox appear a little crazy but he is in fact acting in a brilliant manner to save himself.