Why did the mule refuse to take sides in the argument?

It didn't want to be stubborn about it.

Did You Know?

The joke plays on mules being famously stubborn animals — so it's funny that this one refuses to be stubborn! Mules are actually hybrids, the offspring of a male donkey and a female horse. Despite their reputation for stubbornness, mules are highly intelligent and have a strong sense of self-preservation, which handlers often mistake for obstinacy. They can live up to 50 years!