1
general::
Extremely obstinate, as in He's stubborn as a mule about wearing a suit and tie. This simile evokes the proverbial stubbornness of mules, whose use as draft animals was once so common that the reputation for obstinacy can hardly be as warranted as the term indicates. [Early 1800s]
American Heritage Idioms
2
general::
Phrase(s): *stubborn as a mule [and] *obstinate as a mule
Cliché very stubborn. (*Also: as ~.) • I tried to convince Jake to go to the doctor, but he’s as stubborn as a mule. • For four years, Henry pestered his parents to let him learn the trumpet. They tried to talk him into some other, quieter instrument, but he was stubborn as a mule, and now he has a trumpet.
McGrawhill's American Idioms And Phrasal Verbs