Believe it or not I don't think that is even close to being the case.
A quick search found that an Arleigh Burke-class DDG has ~24 officers and 300 enlisted and a VFA squadron has ~20 or more officers, depending on if it is an E or F squadron, and ~200 or so enlisted personnel. Add up the all carrier, maritime patrol/recon and helo air wings (whose squadrons usually have A LOT more aviators than VFA) along with the large training wings as well (that SWO's don't have) and you get quite a few officers.