Several factors may push a city to offer free bicycles to its residents.
A city may offer free bicycles to its residents in order to reduce congestion on its roads, or on its public transport network.
A city may also offer free bicycles to its residents in order to promote healthy living and physical activity. It has often been argued that riding a bicycle is one of the best forms of physical exercise, and that is indeed something you are likely to find a lot of support for if you visit websites like WebMD or that of Mayo Clinic. And it is in cities’ best interest to promote good health in their residents, because when the residents fall ill, it is the cities that suffer in terms of reduced productivity and other things.
A yet another level, a city may offer free bicycles to its residents in order to reduce pollution. You have to understand that bicycles don’t emit any exhaust gasses, unlike the other forms of motorized transport available to city residents.
While many cities desire to offer the said free bicycles to their residents, the logistics of doing so tend to be a bit complicated. The challenge is that of ensuring that the people who are given the free bicycles are able to return them. That often necessitates the charging of ‘deposits’ which in turn means that the bicycles are no longer free. Then there is also the question of sustainability of the whole program, and the question of how it can be funded on a long-term basis.