mulish (adj.)

"hybrid offspring of donkey and horse," from Old English mul, Old French mul "mule, hinny" (12c., fem. mule), both from Latin mulus (fem. mula) "a mule," from Proto-Italic *musklo-, which is probably (along with Greek myklos "pack-mule," Albanian mushk "mule) a loan-word from a language of Asia Minor.

The mule combines the strength of the horse with the endurance and surefootedness of the ass, and is extensively bred for certain employments for which it is more suited than either; it is ordinarily incapable of procreation. With no good grounds, the mule is a proverbial type of obstinacy. [OED]

Properly, the offspring of a he-ass and a mare; that of a she-ass and a stallion is technically a hinny. The males are ordinarily incapable of procreation. Used allusively of hybrids and things of mixed nature. Meaning "obstinate, stupid, or stubborn person" is from 1470s; the sense of "stupid" seems to have been older, that of "stubborn" is by 18c.

As a type of spinning machine, it is attested from 1793 (as mule-jenny, 1788), so called because it is a "hybrid" of Arkwright's drawing-rollers and Hargreaves' jenny. The underworld slang sense of "narcotics smuggler or courier for a drug trafficker" is attested by 1935. The mule-deer of Western U.S. (1805) is so called for its large ears.

adjectival word-forming element, Old English -isc "of the nativity or country of," in later use "of the nature or character of," from Proto-Germanic suffix *-iska- (cognates: Old Saxon -isk, Old Frisian -sk, Old Norse -iskr, Swedish and Danish -sk, Dutch -sch, Old High German -isc, German -isch, Gothic -isks), cognate with Greek diminutive suffix -iskos. In its oldest forms with altered stem vowel (French, Welsh). The Germanic suffix was borrowed into Italian and Spanish (-esco) and French (-esque). Colloquially attached to hours to denote approximation, 1916.

The -ish in verbs (abolish, establish, finish, punish, etc.) is a mere terminal relic from the Old French present participle.