'nonantagonizable' originates from Latin and Greek elements: the prefix 'non-' (from Latin 'non' meaning 'not') combined with 'antagonize' (from Greek 'antagōnizesthai'/'antagonizō'), plus English adjectival suffix '-able' meaning 'capable of'.

'antagonize' comes into English via Latin and French from Greek 'antagōnizesthai'/'antagonizō' (to contend or oppose); the adjectival form 'antagonizable' would be formed in English by adding '-able' to the verb, and 'non-' was prefixed to create 'nonantagonizable' as a negative adjective.

Initially, the Greek root related to 'striving against' or 'contending with'; over time in English 'antagonize' came to mean 'to provoke hostility or make someone hostile,' and 'nonantagonizable' thus denotes 'not capable of being provoked' in modern usage.