The story
From Aesop's fable The Satyr and the Traveller, in which a satyr declares he cannot trust a man who blows hot (to warm his hands) and cold (to cool his food) with the same breath.
Etymology from Wiktionary, CC BY-SA 4.0.
blow hot and cold
Today it means: To behave inconsistently; to vacillate or to waver, as between extremes of opinion or emotion. Full definition →