Chlorination has been so widely practiced and for so long with what appear to be good results that most people trust it and accept it as the preferred method. But it is also true that chlorine can react with substances in the water to produce carcinogenic compounds, one of the reasons why water treated with chlorine is strictly monitored for the concentrations of these compounds. But as is stated in the article linked below, the dangers of chlorination pale in comparsion to the dangers of untreated or poorly treated water.
The other danger is that chlorine is such a volatile chemical and can be used in the production of poisonous gases and so there are concerns about its possible spill or release into the environment during transport or storage. There is also concern about someone taking advantage of stockpiles at treatment facilities for terrorist action.