I know that for me, it makes sure I apply the same number of strokes to each side. If I lose count, at least I know I did the same number of strokes on each side of the blade. If I did a set of 20 on one side, and lost count on the other, I'd be wearing the blade unevenly. This is a relatively minor issue if you can count, though

Once you get used to it, the grip isn't bad at all. Rolling the spine over almost becomes second nature. I'm sure some honemeisters will chime in with some better reasoning, too.