'apologizer' ultimately comes from the verb 'apologize', which derives from Late Latin and Greek; specifically from Greek 'apologia', where 'apo-' meant 'away' and 'logos' meant 'speech'.

'apologia' (Greek) passed into Medieval and Late Latin as 'apologia', influenced Old French forms, entered English as 'apologize/apologise' in the 16th century, and the agent noun developed as 'apologizer' (US) / 'apologiser' (UK).

Originally it referred to a 'speech in defense' ('apologia'); over time the sense shifted to 'to make an apology', and the noun came to mean 'a person who apologizes'.