Science can't prove anything. No watter how much evidence may exist that something is so, it only takes one counter example to show that it isn't. But that's not a weakness of science, it's the way things work. Our unwillingess to accept it is a weakness in the way we think.
In 17th century Europe the only swans anyone had ever seen were white. In fact, "all swans are white" was used as the standard example of a scientific truth—until 1697, when explorers found Cygnus atratus in Australia— black swans. Here's one I photographed in New Zealand.
The fact is, as Francis Bacon warned, our minds are wired to deceive us. "Beware the fallacies into which undisciplined thinkers most easily fall--they are the real distorting prisms of human nature."
Assuming there's more order in nature than is actually there is something that crops up frequently—faces in clouds, figures in tree bark and peanut-butter, even religious explanations for natural processes such as evolution.
Our brains are wired to understand stories, thanks to the way we evolved. They're not wired to understand uncertainty. So we make up stories to explain complex thing we don't and can't know.
Nassim Nicholas Taleb writes about this in Fooled by Randomness, an fascinating look at why we're inclined to deceive ourselves when it comes to statistics. In The Black Swan: the Impact of the Highly Improbable he looks at how our inability to deal with uncertainty effects our ability to predict, and deal with, the future.
The problem, he writes, is that we place too much weight on past events when simple chance is the best explanation. "History does not crawl, it jumps," he writes, an example of wild power law swings that shape our world.
Important, even earth-shaking events, are rare and unpredictable. Black Swans, he argues, are like the most significant events in our world—rare and unpredictable. So creating stories—conspiracy theories, alien abductions, and religious myths, for example—are our emotionally satisfying but useless solution.