If nothing else, think of it this way. If you're going 15 MPH, which is conservative for a normal cyclists, if you get hit going against traffic, you'll have a 30 MPH faster collision than if you get hit traveling with traffic.
People who travel against traffic think of themselves as pedestrians on wheels, not drivers of vehicles. Given how some people ride, less than 10 MPH and very wobbly, that may be valid for them, but most of us here travel between 15 and 25 MPH, and generally in a very straight line. Given that, your manuverability is probably about that of a moped. Ask the cop if he thinks mopeds should travel against traffic as well. How about any vehicle with the same footprint? How about motorcycles?
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Work: the 8 hours that separates bike rides.