The problem is that for a lot of people, the answer wouldn't really be about business. If they really dug down to think about what their greatest weakness was, they might find it was an issue of character. And those don't go over well in an interview.

What company or government would hire someone who said their greatest weakness was sex addiction, alcoholism, sexism or a vindictive streak? And yet, men such as Bill Clinton, Winston Churchill, Richard Feynman and Thomas Edison have done great work and great things despite those weaknesses.