Arrogant is thinking you are better than other people and making sure they see it. The colleague who talks over everyone, the driver parked across two spaces, the student who corrects the teacher for sport.
It is colder and harder than proud, and it is always an insult — nobody calls themselves arrogant. The noun is arrogance and the adverb is arrogantly. It fits behaviour as well as people: an arrogant tone, an arrogant assumption, arrogant of him to think he was invited. Confident is the compliment; arrogant is what the same energy gets called when it goes too far. There is a rare verb in the family, arrogate, meaning to take something you have no right to.
Latin arrogāns is the -ing form of the verb arrogō, and English still keeps that verb as arrogate. It came through Old French arrogant into Middle English as arrogaunt, and the spelling later settled back towards the Latin.
Latin
arrogāns
Old French
arrogant
Middle English
arrogaunt
English, today
arrogant
From Middle English arrogaunt, from Old French arrogant, from Latin arrogāns, present active participle of arrogō.
Etymology from Wiktionary, CC BY-SA
Practised in Feelings & Character, Moods & Relationships