Your cycling fallacy is…
“People should wear helmets when cycling, that would make it safe”
Wearing a helmet has been shown to make little difference to overall cycling safety. Countries with mandatory helmet laws, or high levels of helmet usage, show no reduction in head injuries (or injuries overall) compared to countries or areas without these laws.
Where streets and roads are designed well, cycling is such a subjectively safe activity that people feel as comfortable cycling as if they were going out in a car, or on a bus, or walking about. Good quality infrastructure has a far higher effect on cycling rates and safety than personal protective equipment.
Conversely, in some parts of the world the environment is so hostile to cycling that many people may feel there is no option but to wear a helmet or other equipment, even if it should only offer the most minor improvement in safety. A high rate of helmet use is a sign that the authorities have failed to design well for cycling.
The mandating of helmet use is proven to have a negative impact: it discourages people from cycling, thus reducing the societal benefit accruing from a healthier, more active population. It should be an individual's choice whether to wear a helmet, or indeed any other form of protective gear.
The effect of good infrastructure cannot be ignored: the Netherlands – which is the safest country in the world for cycling, with the widest demographic of people who cycle – also has the lowest rate of helmet use. Anyone who truly cares about cycling safety should campaign for infrastructure, first and foremost.
Source: P.M. Lydon (CC BY-SA 3.0)