From
this website:
Autopilot Called George
When autopilots first became available, there happened to be a saying, "Let George do it", which was part of a wartime poster that said, basically, that you couldn't do that- you had to do it yourself, or no one would do it. The "Let George do it" attitude was something to be stamped out during the WWII war years, you see...The autopilot was the only "George", or "the other guy", that you could legitimately delegate to. Thus, using the autopilot became "letting George do it".