'anti-state' is a compound of the prefix 'anti-' (from Greek 'anti-' meaning 'against') and 'state' (from Old French 'estat' < Latin 'status', meaning 'condition, position' or, by extension, 'political organization').

'state' entered English via Old French 'estat' and Middle English 'state/estat' from Latin 'status' (originally 'standing, condition'); the prefix 'anti-' comes from Greek 'anti-' and was adopted into English via Latin and French. Combining these elements produced the modern English compound 'anti-state'.

Originally the parts meant 'against' and 'condition/standing' (hence 'political condition'); over time the compound has come to specifically denote opposition to governmental authority or the political state as an institution.