It was also available for centuries before plate was, so a great many more people had the training to make it.
actually, no it wasn't. think about it, it is a fairly common misconception. making a sheet of metal more difficult than making interlocking rings? greeks used bronze to make a cuirass which is too soft to make into decent chain armor. carbon fiber vests were used before that and dubbed linothorax, which is quite different than medieval padded cloth.
First, while Bronze was used in brestplates and far earlier than the medieval period, iron and steel, which replaced bronze due to availability, was a good deal harder to work, as making the large sheet required needs fairly consistent temperatures across the entire surface, which was much tricker due to the higher temps that iron is worked at. Further, once the rings are made, much less skill is needed to assemble them, meaning that much of the labor can be done by apprentices, rather than the expert armorsmith. (I've even come across sources suggesting that whole villages participated in the weaving of mail, but I don't know how reliable those are.) Also, a flaw in plate armor ruins the entire piece, while a few bad links in a coat of mail can easily be replaced.
Taking it even further, mail is lighter and more flexible than plate, meaning that the arms and legs, which in classical times were largely unprotected, going by museum pieces, could be covered at a small penalty in flexibility.