1540s, "used in attack, attacking;" 1570s, "insulting, causing or giving displeasure," from French offensif (16c.) and directly from Medieval Latin offensivus, from Latin offens-, past-participle stem of offendere "offend" (see offend). Sense of "disgusting, disagreeable" (of odors, taste, etc.) is from 1590s. Related: Offensively; offensiveness.
1720, the offensive, "condition of attacking, an aggressive action or course," from offensive (adj.). Military sense of "forceful action toward a particular end" is by 1918, from World War I.