this makes no sense to me at all. when i want to turn left on a bike, i do not turn the wheel to the right. i turn it to the left (left side in).
i agree with oneplankawanka - the bike analogy is, in this context, a simple one which works well.
It's weird to get it at first, but once you understand it, you'll realize that you already knew. You just don't know that you know.