scrubbing (n.)

c. 1400, scrobben, "to rub hard; rub or scratch (someone, an animal)," a variant of shrubben (c. 1300), which is perhaps from Middle Dutch or Middle Low German schrubben, schrobben "to scrub," or from an unrecorded Old English cognate of these, or from a Scandinavian source (such as Danish skrubbe "to scrub"). Probably ultimately from the Proto-Germanic root of shrub, an ancient cleaning tool. Compare the evolution of broom, brush (n.1), also compare scrub (n.1).

Meaning "to cancel" is attested from 1828, probably from notion of "to rub out, erase" an entry on a listing. It was popularized during World War II with reference to air missions. Related: Scrubbed; scrubbing.