'Hand' has been used for a multitude of meanings over time. In the sense of one side of an argument or one set of circumstances as opposed to another, it has existed for centuries. The earliest recorded use of the specific phrase 'on the other hand' dates back to the middle of the 17th century. Basically, of course, the idea comes from the fact that we have a hand on either side of our bodies; hence things like "The left hand doesn't know what the right hand's doing' and so forth.