1620s, "to kick out," from Latin recalcitratus, past participle of recalcitrare "to kick back" (see recalcitrant). Sense of "resist obstinately" is from 1759. Related: Recalcitrated; recalcitrating; recalcitration.
in football, "a kick of the ball as it is dropped from the hands and before it strikes the ground," 1845; from punt (v.).
"to kick a ball dropped from the hands before it hits the ground," 1845, first in a Rugby list of football rules, of obscure origin; perhaps from dialectal punt "to push, strike," alteration of Midlands dialect bunt "to push, butt with the head," of unknown origin, perhaps echoic (compare bunt).
Student slang meaning "give up, drop a course so as not to fail," 1970s, is because a U.S. football team punts when it cannot advance the ball. Related: Punted; punting.