So how DO you hide the resignations of 24 generals? Well, you don't announce the resignations en masse; you spread them out over several months. Which is just what happened. Less than a half dozen of the vacated positions were refilled
OH WAIT THAT WAS DURING THE CLINTON ADMINISTRATION.
NEVERMIND
You also decimate the miliatry by a few divisions. Remember that you don't promote unless there is a job. When you cut the number of ships by 300, a few admirals loose their jobs