This may never be true in the sense that pigs will fly, but the belief that all swans are white has already been disproved. Black swans were discovered in Australia, which shifted many people's ideas of the impossible into the possible.
Some examples of the Black Swan Theory are the invention of the computer, World War 1, and the Attacks on 9/11. These were all events that nobody could have predicted and, when they occurred,
all caused drastic changes throughout the globe. According to this video one of the most important examples of the Black Swan Theory took place was with the discovery of fire. It is highly unlikely that an early human understood the concept of fire, much less how to create it; so we assume that the discovery of fire occurred completely by chance. However, this random chance was crucial in the development of civilizations and societies.
Another aspect of the Black Swan Theory is that each event was always somehow rationalized through the use of hindsight despite the fact that they were all entirely non-rational events. As humans, we find it necessary to come up with reasons for everything, which is why we have science.
This theory does not only concern theories about the colors of birds, it also includes many of the scientific theories that we base our knowledge on today. These ideas we believe in can all be disproved with single pieces of information, causing entire theories to come crumbling down.
Black Swans have been seen in science many times, some examples being the ideas of the theories of relativity and of quantum mechanics against the ideas of classical physics and the discovery of dark matter and dark energy. In both of these instances, something new was discovered that caused the already set ideas to shift. This is an important part of science, but it is also slightly terrifying. To know that all the scientific knowledge we have could be dispelled so easily leads to many more questions. But as they say, good scientists set out to prove themselves wrong.