Punt on 3rd down.

Video here (at 1:55).

The only other conceivable reason for a team to punt on third down, is if a) it’s the last play of the game, with no hope of winning; and b) your punter is one punt short of a record. There are many horrible teams in the NFL this year, for instance. Since their punters always seem to be busy anyway, they might as well shoot for something !