Excellent question! Short answer: metalbending is a sub-discipline of earthbending. Slightly longer answer: Earthbenders used to believe that metal couldn't be controlled, but Lin's mother, who was denied proper training as a child because of her blindness, essentially taught herself from scratch and invented the practice, then went on to start her own school and found the metal-bending police force.

(Also, if it arises, lightning-bending is likewise a sub-discipline of firebending.)