A misspelling of "binary."
Josh: Hey I'm non-binnery
Kyle: Excuse me?
Josh: I mean "binary."
A cooler way to say non binary
Dude 1: "Hey, man. What gender are you?"
Dude 2: "Oh, I'm non binnery."
Dude 1:"I completely understand what you are saying and I shall now bow before you."
Dude 2: ?
Dude 1: "ALL SHALL BOW BEFORE THE ONE WHO EXCEEDS GENDER!"
Dude 2: ?!
INFORMAL> AUS/NZ
Noun: binnery din ; plural noun: binnery dins
Bins
Josh : *hears alarm*
James: Cant forget the Binnery Dins
Josh: I'm on it