early 15c., transitive, "impair (authority); disparage (reputation)," a sense now obsolete, from Latin derogatus, past participle of derogare "to take away, detract from, diminish," also "repeal partly, restrict, modify," from de "away" (see de-) + rogare "ask, question; propose," apparently a figurative use of a PIE verb meaning literally "to stretch out (the hand)," from root *reg- "move in a straight line."
Intransitive sense of "take away a part, make an improper or injurious abatement" is from 1560s; that of "do something that tends to lessen one's honor or rank" is from 1610s.