When two generally stubborn people decide to be stubborn in an argument for no other reason than the challenge of it. People will irrationally stick to their point of view no matter what evidence is presented.
Person 1: Ryan and Lisa are arguing about whether the holocaust was real or a hoax

Person 2: Ohh look now they are ignoring each other again, neither will agree.

Person 1: Yah they are having another Stubborn-Off what a stupid fight. Everybody knows aliens committed the holocaust.
by MuffinCrunchers January 1, 2012
Get the Stubborn-Off mug.