Heavy anchors can smash even the most sturdy corals, while the anchor chains and line can scrape coral, removing living tissue, and can wrap around corals and break off pieces of coral colonies - or even entire colonies - as the boats sway back and forth and pull on the line. So anchor in the sand or mud, NOT in the coral.
It's pretty simple - in a contest between anchors and coral, anchors win every time. Boat anchors can cause significant physical damage to corals, especially at reef sites that receive a lot of boat traffic - like diving or snorkeling sites. So anchor in the sand or mud, NOT in the coral.