Chlorine kills the beneficial bacteria and also burns the fish's gills and skin. Just because bettas can breathe air doesn't mean they should have to on a regular basis - its an emergency survival skill, they are not air-breathers by choice.
Yes the labrimth is not exactly an emergency organ but a vital one...anyways this doesn't mean they can live in chlorinated water like anna said In fact scientits removed a labrimth from a betta and it couldn't survive without one
its true that a betta can live in cholinated water didnt about 2 years ago w/o knoing any ting about nettas except they will fight with eachother. but i dont think they would like to live in chlorinated water.