1560s, "relation of parts, proportion," from French symmétrie (16c.) and directly from Latin symmetria, from Greek symmetria "agreement in dimensions, due proportion, arrangement," from symmetros "having a common measure, even, proportionate," from assimilated form of syn- "together" (see syn-) + metron "measure" (from PIE root *me- (2) "to measure"). Meaning "harmonic arrangement of parts" first recorded 1590s.
word-forming element meaning "excessive or irrational fear, horror, or aversion," from Latin -phobia and directly from Greek -phobia "panic fear of," from phobos "fear" (see phobia). In widespread popular use with native words from c. 1800. In psychology, "an abnormal or irrational fear." Related: -phobic.
<a href="https://www.etymonline.com/word/symmetrophobia">Etymology of symmetrophobia by etymonline</a>
Harper, D. (n.d.). Etymology of symmetrophobia. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/symmetrophobia