It is realistic to try to avoid putting myself in a position where I may avoid being hit or run over by a car with no steel or anything to protect me. And we are making massive strides in terms of safety with things like self-driving cars.
You may know that risk can qualitatively be thought of as a product of two factors: the severity of the outcome and the probability of occurrence.
In the case of cycling a high-speed rear collision with a car is very unlikely but very severe in its outcome. How common is this accident? Not very common-- it ends up on the news when it does occur.
Many many cyclists enjoy riding, on the street, for their whole lives and never have a serious accident or injury.
People fly by you in their car, inches away, while on the street on a regular basis, and you have no control over this. On a sidewalk, I have to be more observant, but more accidents there will be avoidable if I am paying attention.
Heard this a thousand times and I don't buy it for a second. The speed differential between cyclists and pedestrians is an order of magnitude different than the speed differential between cyclists and cars. And the argument about driveways and intersections falls 100% flat on it's face if you use the incredibly basic assumption that cyclists should (a) use crosswalks and (b) shoulder check when crossing driveways.
A pedestrian walks at around 3 to 4 mph. A cyclist can ride at 15 to 20 mph. Cars on suburban streets can go 25 to 40 mph. That's about a 12 to 16 mph difference between a pedestrian an a cyclist and a 5 to 25 mph difference between cyclists and cars.
What is also important is the nature of the collision. A glancing (side-swipe) collision, is very different from a direct collision. Also in right-hooks, the most common collision of all, you have a cyclist colliding with a slowly turning car while typically braking and turning at the same time.
But even if we're talking about direct collisions, the cyclist often ends up going over the hood or roof of the car simply because of the height of the bike vs the car. This looks awful but is actually better than hard impact.
There are more factors than mass and speed differences.
Cycling is not particularly dangerous, depending on how you define "dangerous".
Most car-bike collisions occur at intersections and are "right-hooks". This is when a car turns right, cutting across the path of the the cyclist and the cyclist hits the car because there's not enough room to stop or turn. These accidents typically result in bruises, damage to bike and sometimes a broken collarbone. They're rarely fatal unless the right-turning vehicle is a truck and the cyclist ends up under the truck.
The accident you're probably thinking of is a car hitting a cyclist from behind with a huge difference in speed. This, I believe, results in the most fatalities for car-bike accidents. It is relatively rare.
None. You have no chance to be truly safe. That's an unrealistic goal for any kind of traffic system.