Extremely obstinate or unwilling to change one's mind or course of action, often unreasonably so.
This phrase emerged in American English during the 19th century when mules were commonly used as working animals. Mules, being hybrids of horses and donkeys, were notorious for their strong-willed nature and refusal to move when they didn't want to.
The comparison is actually quite accurate from a behavioral standpoint - mules are indeed more cautious and strong-willed than horses, often refusing to proceed if they sense danger. This trait, while frustrating to handlers, actually made them valuable pack animals in treacherous terrain because their 'stubbornness' often prevented accidents.
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