Expression used when attempting to convince someone to have a second drink. For example:

DRUNK 1 : (on finishing first pint) "Okay then, I'm off home for dinner"
DRUNK 2 : "Ah stay and have another. Just the one."
DRUNK 1 : "No, really, I can't."
DRUNK 2 : "Come on. A bird never flew on one wing."
DRUNK 1 : "...fair enough then. Guinness there please Mike."

And so on. Rumour has it that a group of alcoholics are currently scouring Western Africa in an attempt to find an 18-winged bird.