First of all, "paired" simply refers to fins that there are a matching set of, like the pectoral fins located at the front of a fish's body. Gill arches are curved pieces of bone or cartilage, each of which supports one of the actual gills. Back in the late 1800s, German anatomist Karl Gegenbaur postulated that paired fins evolved from the gill arches, since the arches appear earlier than the fins in the fossil record.