Within the show, elements could be manipulated using specific movements. Earthbenders make rigid and heavy movements, because earth is rigid and heavy; you wouldn't be able to bend earth using fluent movements, because earth isn't fluid. Bending isn't martial arts, rather, it's a means of manipulating elements. The movements themselves aren't meant for fighting by manipulating your body, but rather, manipulating the elements around you. Chiblocking, however, is classified as a martial art as they use jabs, punches and kicks that connect with the enemy's body.
Production-wise, martial art styles were picked that resembled the elements closest: tai chi for its fluid forms, a certain style of kung fu for its rigid style and solid footing, etc. They are purely used for aesthetic purposes, and what their movements represent.
Also, something that wasn't noted in the first post is that bending originated from lion turtles.