The expression is used to describe someone who is inconsistent. Charles Dunk explains in his book “A Hog on Ice & Other Curious Expressions” that the expression comes from one of Aesop’s fables. A satyr “…comes upon a traveler in winter who is blowing on his fingers.” The traveler explains he is doing that to warm his fingers. The satyr then offers the traveler hot soup, and the man blows on it. When asked whether the soup is not hot enough, the man explains he is trying to cool it. The satyr orders the man to leave with the admonition, “I will have no dealings with one who can blow hot and cold from the same mouth.”