this is the one slot i have to hire a person for at least the next six months to help me prop up my project. i usually have an hour to try to figure out whether we are going to be able to work together productively and whether this person has the knowledge and the inclination to do that, or really anything.
so we can get up at the whiteboard and solve a problem or two together, and i can see how this person works, or we can chat about their personal situation and trade jokes. what does this non-technical interview really accomplish?
it's not a test. this isn't school. i want to see your exposed thought processes and make a very mercantile decision. if that offends you then i probably dont want to work with you anyways. if you are a programmer then it really shouldn't bother you at all to spend time working through fictional problems.
and if they are hard enough, its usually pretty fun for both of us.
Maybe they started when whiteboards became widely distributed. In other words, we do them because we can.