1650s, "the study of the soul," from Modern Latin psychologia, probably coined mid-16c. in Germany by Melanchthon from Latinized form of Greek psykhē "breath, spirit, soul" (see psyche) + logia "study of" (see -logy). The meaning "science or study of the phenomena of the mind" is attested by 1748, in reference to Christian Wolff's "Psychologia empirica" (1732). The modern behavioral sciences sense is from the early 1890s.
word-forming element used to make verbs, Middle English -isen, from Old French -iser/-izer, from Late Latin -izare, from Greek -izein, a verb-forming element denoting the doing of the noun or adjective to which it is attached.
The variation of -ize and -ise began in Old French and Middle English, perhaps aided by a few words (such as surprise, see below) where the ending is French or Latin, not Greek. With the classical revival, English partially reverted to the correct Greek -z- spelling from late 16c. But the 1694 edition of the authoritative French Academy dictionary standardized the spellings as -s-, which influenced English.
In Britain, despite the opposition to it (at least formerly) of OED, Encyclopaedia Britannica, the Times of London, and Fowler, -ise remains dominant. Fowler thinks this is to avoid the difficulty of remembering the short list of common words not from Greek which must be spelled with an -s- (such as advertise, devise, surprise). American English has always favored -ize. The spelling variation involves about 200 English verbs.
<a href="https://www.etymonline.com/word/psychologize">Etymology of psychologize by etymonline</a>
Harper, D. (n.d.). Etymology of psychologize. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/psychologize