'anti-galactic' is formed from the Greek-derived prefix 'anti-' (from Greek ἀντί) meaning 'against' and 'galactic' (from Greek 'galaxias' / 'galakt-' meaning 'milk', used for the Milky Way).

'galactic' entered English via Late Latin/Medieval Latin (e.g., Latin 'galacticus') and Old French forms derived from Greek 'galaxias'; the productive prefix 'anti-' has Greek/Latin roots and has been used in English compounds since Middle English. The compound 'anti-galactic' appears as a modern coinage, especially in 20th century science-fiction and technical discourse.

Individually, 'galactic' shifted from the Greek sense tied to 'milk' (the Milky Way) to 'relating to a galaxy'; combined with the productive prefix 'anti-', the modern coinage 'anti-galactic' has come to mean 'against or outside the galaxy' (literal or figurative), a usage developed in contemporary contexts.