Apologize

google

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late 16th century (in the sense ‘make a defensive argument’): from Greek apologizesthai ‘give an account’, from apologos (see apologue). In English the verb has always been used as if it were a direct derivative of apology .

wiktionary

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apology +‎  -ize, from  ἀπολογία(apología, “a speech in defense”), from  ἀπολογέομαι(apologéomai, “to speak in one’s defense”), from  ἀπόλογος(apólogos, “an account, story”), compound of  ἀπο-(apo-, “from, off”) and  λόγος(lógos, “speech”); compare also  ἀπολογίζομαι(apologízomai, “to render an account”). 

etymonline

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apologize (v.)

1590s, "to speak in defense of;" see apology + -ize. Sense of "regretfully acknowledge" is attested by 1725. The Greek equivalent, apologizesthai, meant simply "to give an account." Related: Apologized; apologizing; apologizer.