Why: Imagine, if you will, that you are the United Kingdom during World War II. Across the Channel, all your allies are knuckling under to an intractable, tyrannical force. Your cities are being cratered by the Luftwaffe, and your ports are being choked by the Kriegsmarine. You realize, in your heart, that you do not have long to live, unless you can think your way out of this fix. But you have something the Nazis do not: you have Alan Turing. You see this man at Cambridge, and you watch him hypothesize a concept called the Turing machine, which could perform any conceivable mathematical calculation far faster and more accurately than anyone alive, even him. So you move him to Bletchley Park, where you surround him with more geniuses and ask him to break the Nazis' Enigma and Lorenz code machines, with their multiple encryptions and their constantly rotating keys. And so he does. He saves your lives. You give him your highest medal. But he doesn't stop there. At the National Physics Laboratory, he designs the first stored-program computers, and creates the Turing Test standards for artificial intelligence. You are on your way to becoming the greatest information superpower in the world. And then you quite literally lose your mind. Investigating a break-in at Turing's house in 1952, your police discover Turing is in a homosexual relationship. You've defined this as illegal, and so you threaten to imprison him (remember, he's the victim of this crime you're investigating) if he doesn't start taking your destructive hormone treatments. And so, in 1954, misshapen and addled from your drugs, he kills himself. You profess to not understand why.
Impact: You, the formerly Great Britain, lose the race to your ally, the United States. Unhindered by competition, the U.S. makes every great computational breakthrough of the 1950s and beyond. You are left behind. But what if you hadn't killed Alan Turing? What if his Manchester Mark I had led to the Manchester Mark XII? What if your later computers had not only met the Turing Test, but met whatever new standards his unbridled mind could create? What if? You'll never know, I guess. But you can take comfort in Santayana's rule. Our newborn empire isn't capable of being high and mighty on this subject. Maybe we'll get to watch some more tolerant country's genius bury us in the next great race.
Personal Connection: I didn't know the full story of Turing's contributions to Bletchley Park until reading Simon Singh's The Code Book this week. And I also didn't know what happened to him after inventing the Colossus and the Mark I. Both developments shocked me. When the history of the computer age is written, persecuting Turing will go down as the dumbest business move of all time.
Other Contenders: well, if you don't want to support gay rights because it's in your best business interests, or because gay people are creative too, how about just because it's the right thing to do?