Inexperienced divers damage coral, but parrot fish eating coral doesn't do damage?
You are absolutely correct in regards that marine life does cause damage to corals. In particular, parrotfish have been found to play an important role in regulating the biodiversity of coral reefs through their feeding behavior. Certain species of parrotfish feed on certain species of coral, typically faster growing species that branch out into easier access bits of corals that the fish can consume. This has the effect of allowing slower growing species that may also be harder corals to consume (in terms of hardness, shape accessibility, or other factors) to grow and compete in the coral reef and prevent the reef from being overgrown with the faster species. A similar process is seen on the land with grazing herbivores which help propagate biodiversity by consuming certain plant species thereby giving increased chances for other species to grow. These ecosystems and the relationships between corals and species like parrotfish have had an extremely long time to come to shape through evolutionary pressures on both sides of the organisms, consumer and producer.

The problem with divers who cause damage to corals is that it is an introduction of artificial stress and arbitrary damage to the coral reef in a short time without much time to adapt, placing additional stress on the environment which is already stressed. Unlike the parrotfish, divers may not discriminate on what corals they damage. Additionally, areas where inexperienced divers damage coral generally will see more inexperience divers often at the same diving site, so from the standpoint of protecting the coral reef, minimizing the damage caused by divers becomes an important priority to the stewards of those areas and the diving shops which bring divers to those areas.