Admirals don’t command ships. Only Captains.
Smaller ships, known as “small boys,” are usually commanded by senior 0-5 surface warfare officers. Carriers are typically commanded by a senior 0-6 aviator. Carrier Strike Groups are groups of deployed ships and submarines that are typically commanded by an Admiral. The most senior ship in the carrier strike group, i.e., the carrier, holds the Admiral and his staff and is known as the flag ship.
The upshot of this is that the Admiral and the Captain were on the same ship. As a retired Navy officer, my educated guess is that the Captain went to the Admiral and the Admiral overruled him, whereupon he wrote the infamous letter and released it to the press.
There is a procedure for the Captain to appeal to higher authority that doesn’t involve revealing to the world the readiness (or lack thereof) of his carrier. IOW, if Crozier didn’t like the Admiral’s decision, he could take it higher privately, and possibly get it overruled. Instead he decided to whine to the world about it. That is an egregious violation of OPSEC.
He’ll be lucky if being allowed to retire at current rank is the worst thing that happens to him.
“ Admirals don’t command ships. Only Captains.”
Yeh, I looked it up.