Coat Hooks Need To Be Fastened To Something Solid

You should never fasten a coat hook to drywall.

There is just too much leverage from the weight hanging on the hook. Even if you screw into a stud behind the drywall, the hook will not fall off the wall, but it will get loose as the bottom of the base plate gets indented into the drywall by the weight on the hook.

You need something solid to mount the hooks to. Some kind of board usually does the trick.