Pet birds are loud, obnoxious animals that never shut the fuck up and that seriously harsh the vibe of any social gathering with their screeching orations. You'd be pissed too if you knew how to fly but were stuck in a cage.

Calm your bird means stop freaking out like a caged bird and harshing the vibe. Either shut the fuck up, or go be free elsewhere.
Joe: "MAN DO YOU SEE THAT GUY? I THINK HE LOOKED AT ME MAN. I THINK HE WANTS TO SAY SOMETHING. I'M GONNA GIVE IT TO HIM. I'M GONNA PUT MY FIST RIGHT UP HIS ASS!"

Cool Pete: "Joe. JOE. You're high on acid and cocaine and you saw yourself in the mirror. Calm your bird."
by LicensesToStone April 30, 2016
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