'antagonise' originates from Greek, specifically the word 'antagonizesthai'/'antagonistes', where 'anti-' meant 'against' and 'agōn' meant 'contest' or 'struggle'.

'antagonizesthai' (Greek) passed into Late Latin and Medieval Latin forms such as 'antagonista' and was adopted into English via French and the suffix '-ize' to form 'antagonize/antagonise' in modern English.

Initially it meant 'to act as an opponent or contend', but over time it evolved to the common modern sense 'to provoke hostility; to make someone hostile'.