When I started road running in junior high, I was running with traffic. The rest of the team was running against traffic. I got told that running with traffic was wrong because it would potentially confuse drivers when I might pass the other runners who were running against traffic. Because then they would see runners approaching them on both sides of the road and be confused as to how to respond.
And thus, my quandry, it would probably confuse oncoming drivers to see cyclists approaching them in both lanes. Right?