A "Jay" in british English is slang for an ignorant or dumb person.
When they wanted to convince people ~100 years ago that streets weren't for pesky carts and peasants, that they were for cars, the automobile industry began this campaign of "Jaywalkers", people who just "got in your machine's way".
Then it moved onto teaching kids the most important lesson of all: look both ways before you cross!. People from back then would find it insane all the space we give to cars.