"rub hard," early 15c., earlier shrubben (c. 1300), perhaps from Middle Dutch or Middle Low German schrubben "to scrub," or from an unrecorded Old English cognate, or from a Scandinavian source (such as Danish skrubbe "to scrub"), probably ultimately from the Proto-Germanic root of shrub, used as a cleaning tool (compare the evolution of broom, brush (n.1)).
Meaning "to cancel" is attested from 1828 (popularized during World War II with reference to flights), probably from notion of "to rub out, erase" an entry on a listing. Related: Scrubbed; scrubbing.
adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy).
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<a href="https://www.etymonline.com/word/scrubby">Etymology of scrubby by etymonline</a>
Harper, D. (n.d.). Etymology of scrubby. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/scrubby