'euphemize' originates from Greek, specifically from the verbal idea behind the noun 'euphemism' (Greek 'euphēmismos'), where the prefix 'eu-' meant 'well' or 'good' and 'phēmē' meant 'speech' or 'utterance', and the English verb was formed with the suffix '-ize' (via Latin/French verbalizing patterns).

'euphemize' developed in English by attaching the verb-forming suffix '-ize' to the noun 'euphemism' (itself from Greek 'euphēmismos'); the noun entered English earlier, and the verb form emerged later (modern English 'euphemize').

Initially related to the idea of 'speaking well' or using 'good words', the usage shifted to the modern sense of deliberately choosing milder or indirect expressions to lessen perceived harshness or offense.