1510s, "refuse, reject" someone or something, a sense now obsolete, from French réfuter (16c.) and directly from Latin refutare "to drive back; rebut, disprove; to repress, repel, resist, oppose," from re- "back" (see re-) + *futare "to beat" (from PIE root *bhau- "to strike").
The meaning "prove (someone) wrong, prove (someone) to be in error, disprove and overthrow by argument or countervailing proof" is from 1540s; of statements, opinions, etc., by 1590s. Many have frowned on the subtle shift in meaning towards "to deny," as the word has come to be used in connection with allegation. Related: Refuted; refuting.
For people who still use the word in its older sense it is rather shocking to hear on the B.B.C., which has a reputation for political impartiality, a news-report that Politician A has refuted the arguments of Politician B. [Charles L. Barber, "Linguistic Change in Present-day English," 1964]