Also, cycling generates a lot of positive externalities (or maybe it eliminates a lot of negative externalities). As such, the free market provides less than the socially optimal level of cycling. Everyone could be better off if the government provides infrastructure and/or education that makes cycling more feasible.
Bikes take way less space to park. They make people more active and could play a large part in the fight against obesity and health problems (that won't have to be taken care of by government funded health programs). Cyclists reduce congestion for cars. They're not burning fossil fuels so they don't create that sort of pollution.
