Cyclists don't just conflict with cars, they conflict with Pedestrians.
I've been hit by cyclists more than once. (And OK, I hit a pedestrian when I was riding a bike back when I was a teenager too.)
Walking in L.A. I experience near-misses with cyclists riding illegally on the sidewalk about as often as I experience near-misses from people running red lights when I'm in a car.
I guess there are not enough bike lanes?
I had a friend in college hit by a bike while he was walking on the sidewalk. There was a clear area for the biker to ride other than the sidewalk. Serious recovery time was required (almost blew his whole semester).
When I'm driving, I hate cyclists, and when I'm cycling I hate drivers. Both groups are filled with complete freaking idiots who shouldn't be allowed onto the roads under any circumstances.