Why is it safer to bike with traffic, instead of facing oncoming cars?
I found this article which has some statistics on accidents involving wrong-way cycling:




  Table 4 shows that all categories of bicyclists traveling against the direction of traffic flow are at greatly increased risk for accidents—on average 3.6 times the risk of those traveling with traffic, and as high as 6.6 times for those 17 and under. This result is readily explained: because motorists normally scan for traffic traveling in the lawful direction, wrong-way traffic is easily overlooked. To give only a single example, a motorist turning right at an intersection scans to the left for approaching traffic on the new road, and cannot see or anticipate a fast-moving wrong-way bicyclist approaching from the right.