As you already may know, "the windy city" was actually a phrase used by the city of Chicago to promote their breezey beaches. LATER, a writer for the New York times used it as an insult for the boastful manner of Chicagoans during the world's fair. It has also been used to describe their politicians, whose lies and false promises have lead people to say they are "full of wind."
So if a know-it-all tool says to you, "You know, Chicago isn't called 'the windy city' because it's windy," you can say, "Fuck you. Yes it is."
Chicago is the windy city. Most people think it's called the windy city because it's so cold during the winter. The nickname originally came about during the 1850 world's fair which was held in Chicago. News spread to New York City from Chicagoans about how grand the world's fair was. Thus, the New Yorkers called Chicago the "Windy City" because of how Chicagoans bragged about the fair and how fast the word got around.
I'm ghetto but I'm informed. I'm from the Windy city.