'anti-polygamy' is formed from the prefix 'anti-' (from Greek anti- meaning 'against') + 'polygamy' (from Greek 'polugamia', where 'poly-' meant 'many' and 'gamos' meant 'marriage').

'polygamy' comes from Greek 'polugamia' → Latin/medieval scholarly usage → entered English as 'polygamy'; the prefix 'anti-' entered English via Latin/French from Greek and is used to form compounds like 'anti-polygamy'.

Initially it literally meant 'against many marriages'; over time it has come to denote organized opposition, legal positions, or ideological stance against polygamous practices.