'anti-political' is a Modern English compound formed from the prefix 'anti-' (from Greek 'anti' meaning 'against') plus 'political' (from Late Latin/Old French via Greek 'politikós').

'political' comes via Old French 'politique' from Latin 'politicus' and Greek 'politikós' (relating to citizens or the polis); 'anti-' is from Greek 'anti' meaning 'against'. These elements combined in Modern English to form 'anti-political'.

Initially, compounds with 'anti-' simply indicated opposition ('against politics'); over time 'anti-political' has been used both to mean actively opposed to politics and to describe deliberate avoidance of political content, giving it a slightly broader modern usage.