There's no doubt that kids were scratching their initials into the walls of the Roman Colosseum and hastily sketching a penis or two on the sides of Greek temples. Kids love to draw penises and boobs. That's just a fact.
But organized street art as we now know it didn't come into existence until much more recently. A lot of different things factored into the rise of modern graffiti in the US and New York in particular. There were socioeconomic factors and political statements to be made and even just the advent of new developments in the supplies and the mediums (like subway cars) that artists could use all contributed to the growth in the form. Political and social commentary has always been a part of public art, but sometimes it's simply about the work. In many ways, one of the most exciting things that street artists have done is the way that they have built a community that exists on its own terms, thus bypassing the establishment and keeping the art their own.