Recalcitrant comes from Latin, literally meaning "kicking back" or "kicking with the heel", from re- (back) + calcitrare (to kick), which itself comes from calx (genitive calcis😞 (heel).  The word entered English via French in the late 18th/early 19th century, describing someone stubbornly resistant to authority, like a horse kicking at its rider, and by extension, a disobedient person. 

According to the Oxford English Dictionary (OED), the word "recalcitrant" first appeared in English in the late 1700s, with the earliest known use in 1797, in writings by an "English Lady", notes this OED entry.  It came from French (récalcitrant) and via Latin and was used in English as a French word before becoming fully naturalized.  It was Initially used to describe stubborn animals, but was later applied to  people that refused to submit, or were disobedient, or stubborn. 

Examples of "recalcitrant" used in a sentence: 
"Everyday I see casual violence meted out on recalcitrant toddlers."
"For the recalcitrant, reformers might propose a variety of modest steps." 
"The town bully was a stiff-necked recalcitrant and all-around troublemaker." 
"The teacher was assigned to deal with a class of recalcitrant fifteen-year-old students."
"She has compared recalcitrant education officials to children who need to be disciplined." 
"There wasn't any doubt it displeased Napoleon that Mme de Stael should show herself recalcitrant to his influence." 

Just the facts:

RECALCITRANT Definition & Meaning - Merriam-Webster

RECALCITRANT Synonyms: 142 Similar and Opposite Words | Merriam-Webster Thesaurus

Examples of 'RECALCITRANT' in a Sentence | Merriam-Webster