The word insolent comes from Latin insolēns, meaning "unaccustomed, unusual", combining the negative prefix in- ("not") with solēns, the present participle of solēre ("to be accustomed").  It entered English through Old French in the 14th century, evolving from meaning "strange" or "unfamiliar" to specifically describe "rude, arrogant, or disrespectful behavior" that disregards social norms and authority, essentially acting "out of custom". 

According to the Oxford English Dictionary (OED), the word insolent first appeared in English around 1386, notably in Geoffrey Chaucer's writings (like the Parson's Tale), meaning someone contemptuous or proudly disdainful of others, originating from Latin.  The sense of "contemptuous of rightful authority" became common later, around the 1670s. 

Examples of "insolent" in a sentence: 
"His insolent stare made her feel disrespected and angry." 
"With an insolent grin, the villain ignored the hero's warnings. 
"She couldn't tolerate his insolent remarks and told him to leave." 
"The captain punished the insolent soldier for talking back to his superior."
"The new employee's insolent attitude towards the manager quickly got him fired." 
"This shows how Kate has a mistaken identity because she appears rude and insolent." 

Just the facts:

INSOLENT Definition & Meaning - Merriam-Webster

INSOLENT Synonyms: 174 Similar and Opposite Words | Merriam-Webster Thesaurus