The story
Possibly an allusion to the abrupt manner in which a swimming duck can dive and disappear beneath the surface of the water, or from duck (“lower the head or body”) as to avoid notice.
Etymology from Wiktionary, CC BY-SA 4.0.
duck out
Today it means: To depart quickly or exit abruptly, especially in a manner which does not attract notice and before a meeting, event, etc. has concluded. Full definition →