carpet (n.)

late 13c., carpet, carpete, "coarse cloth;" mid-14c., "tablecloth, bedspread;" from Old French carpite "heavy decorated cloth, a carpet" (Modern French carpette), from Medieval Latin or Old Italian carpita "thick woolen cloth," probably from Latin carpere "to card, pluck" (from PIE root *kerp- "to gather, pluck, harvest"). Thus it is so called because it was made from unraveled, shredded, "plucked" fabric. The English word is attested from 15c. in reference to floor coverings, and since 18c. this has been the main sense. The smaller sort is a rug.

Formerly the carpet (usually in a single piece, like the Persian carpet) was also used (as it still is in the East) for covering beds, couches, tables, etc., and in hangings. [Century Dictionary]

From 16c.-19c., by association with luxury, ladies' boudoirs, and drawing rooms, it was used as an adjective, often with a tinge of contempt, in reference to men, as in carpet-knight, 1570s, one who has seen no military service in the field; carpet-monger, 1590s, a lover of ease and pleasure, i.e. one more at home on a carpet.

On the carpet "summoned for reprimand" is by 1900, U.S. colloquial (but compare carpet (v.) "call (someone) to be reprimanded," 1823, British servants' slang). This may have merged with older on the carpet "up for consideration" (1726) literally "on the tablecloth," with the word's older sense, hence "a subject for investigation." To sweep or push something under the carpet in the figurative sense is recorded by 1953.

1620s, "cover with or as with a carpet," from carpet (n.). The meaning "call to reprimand, make a subject of investigation" is from 1823. Related: Carpeted; carpeting.