Most of the answers boil down to depends where you live. When I lived in Denver there were tons of bike only trails, the air was usually great, and lots of people biked. Biking there was a way of life for many people.
Where I live now, the air is great, but there are few if any bike lanes. Yet, I still see cyclists going down 2 lane roads with traffic going by them at 50MPH. An accident is bound to happen, and over the summer a cyclist was hit on one of the bridges. He flew off the bridge, and fell to his death. It is common sense that cycling on busy roads is more dangerous than driving a car on the same road.
The accident statistics do not back up your assertion. Most cyclists are injured when turning from the wrong lane or when using bike paths or sidewalks. When you're on the road with the rest of the vehicles, people pay attention to you because they have to check to be sure that a car is not where you are. (There are bad drivers, but you have better maneuverability and brakes than them.)
Americans are taught at an early age to be afraid of riding their bikes on the street, but there is really nothing scary about it. And drivers aren't as bad as you think they are: when there is something in their path, they tend to steer around it.
The issue is not that bicycling is hazardous; the issue is that drivers are inattentive.
Here in the UK, around 90% of road traffic accidents are attributable to driver error.
We badly need to reach the era of self-driving cars, so that folks who'd rather be checking their email can do so without endangering the rest of us, and so that cyclists can ride the highways safely again (or at least as safely as they did prior to 1910 or thereabouts).
Where I live now, the air is great, but there are few if any bike lanes. Yet, I still see cyclists going down 2 lane roads with traffic going by them at 50MPH. An accident is bound to happen, and over the summer a cyclist was hit on one of the bridges. He flew off the bridge, and fell to his death. It is common sense that cycling on busy roads is more dangerous than driving a car on the same road.