Then I assume you wouldn't object to having mandatory liability insurance to cover any damage and/or injury you cause as a cyclist.
I have worked as firefighter for over twenty years. I have been to dozens of cyclists who have been hit by cars and trucks including fatalities and very serious injuries. In every case that I can remember the incidents have been caused not by the cyclist but by an inattentive or otherwise negligent driver. The majority of times the cyclists have been struck from behind with no warning while they have been riding along the right side of the road where they are suppose to be and not obstructing traffic in any appreciable way. These accidents I have been to have mostly been on side streets and not main thoroughfares.
I have never been to an incident where a cyclist has been found to have contributed in any way to property damage or the injury of another person. Forcing cyclists to have mandatory liability insurance is a solution to a problem that does not exist. The chances of a cyclist causing injuries or damage to others is so low that the price of such a policy would basically only have to cover administrative costs. I am a general aviation pilot; people are always surprised to learn that the cost of insuring our plane is less than the cost of insuring our ten year old car. The chance of causing damage to persons other than those riding with you in a small plane are astronomically low.