'antioptimistically' originates from Modern English, formed by the Greek-derived prefix 'anti-' (from Greek 'anti' meaning 'against') plus 'optimistically' (from 'optimistic' from Latin root 'optimus' 'best' via French/English developments), with the adverbial suffix '-ally'/'-ly'.

'antioptimistically' developed from the adjective phrase 'anti-optimistic' (a compound using the prefix 'anti-' + 'optimistic') which then acquired the regular adverbial ending to become 'antioptimistically' in modern usage.

Initially formed to mean 'against optimism' in a descriptive sense; it has retained that core sense and is used to describe actions or attitudes expressed in an anti-optimistic (or pessimistic) way.