1640s, "vindicatory, containing a defense," from French apologétique, from Latin apologeticus, from Greek apologetikos "defensible," from apologeisthai "speak in one's defense," from apologos "an account, story," from apo "away from, off" (see apo-) + logos "speech" (from PIE root *leg- (1). The meaning "regretfully acknowledging failure" is by 1836 (apologetic for himself).
in the names of sciences or disciplines (acoustics, aerobics, economics, etc.), a 16c. revival of the classical custom of using the neuter plural of adjectives with Greek -ikos "pertaining to" (see -ic) to mean "matters relevant to" and also as the titles of treatises about them. Subject matters that acquired their English names before c. 1500, however, tend to be singular in form (arithmetic, logic, magic, music, rhetoric). The grammatical number of words in -ics (mathematics is/mathematics are) is a confused question.
<a href="https://www.etymonline.com/word/apologetics">Etymology of apologetics by etymonline</a>
Harper, D. (n.d.). Etymology of apologetics. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/apologetics