The unicycle actually predates the "safety bicycle", the basis of most bikes today. Penny Farthings had a somewhat unnerving tendency to flip over forwards easily, because of the rider being so high up and with little weight over the back wheel.
Some riders learned to lessen the chance of being launched in such a dramatic manner by riding it with the back wheel off the ground; when braking the rider retained the "buffer zone" of being able to lean back, unlike riders using both wheels. Inevitably this led to people removing the back wheel altogether, and simply riding the remaining wheel by standing on the pedals and holding on to the handlebars.