It turns out that motorists are assholes...at least everyone is more of an asshole when they are behind the wheel. You can be a nice person, but get behind the wheel of a car and you feel somehow empowered. You are more susceptible to road rage and you're in a killing machine. Driving is a dangerous, expensive habit. Drivers don't care about paying full attention to the road. They send text messages and eat hamburgers while they reach for something they dropped and change the radio station. Drivers view their license as a birth right, not a privilege.
Let me also take this time to say that some cyclists are assholes. They run red lights and flick off cars who go on green. They ride on the left side of the street. They don't have reflectors or lights and ride in the dark. They slowly cross the road in front of oncoming traffic. Some of the ill will of drivers toward cyclists is engendered by this behavior.
If we had more bicycle infrastructure and made it feasible for people who aren't quite as extreme as me to get around using two wheeled transportation, then we could drastically lower the prevalence of accidents like this while reducing obesity and pollution. We would lower health care costs and road maintenance costs. Bikes are much lighter than cars and you can fit way more of them into the same area. A parking spot for one car can hold 6+ bikes. Likewise a lane for moving traffic can hold way more bikes than cars. Also, people I know who drive despise their commute (except for some motorcycle drivers I know). Cyclists generally enjoy their commute. If more of your colleagues biked to work, there would be a friendlier work environment and probably higher productivity too.
In many cases it's just as fast to cycle or cycling can add 3-5 mintues to a trip. Not much time is lost by cycling. Everyone can win. Get more people on bikes and cars can have less traffic to contend with. The question is "how do we shift the paradigm?"