Asinine is an adjective formed from the Latin asininus, meaning "like an ass", but more specifically, like an ass in the sense of failing to exercise intelligence or judgment.
The ass has long been a symbol of ignorance. Examples can be found in Aesop's Fables, Apuleius's The Golden Ass[?] (The Metamorphoses of Lucius Apuleius) and Shakespeare's Midsummer Night's Dream.