I havent followed it as closely as some, but I heard he jumped the chain of command.
If true, it is one thing to have attempted to engage your immediate superiors (better have solid documentation) with no result before you go above their heads, and quite another thing to have just jumped them.
If that is the case that he just jumped them, that is a fireable offense right there.
And rightly so, IMO.
I understand his superiors were already acting on the coronavirus on ship so he would have to be aware of that as Captain. This sounds to me like he went rouge and acted on his own.
There is a lot less to that than meets the eye. As carrier CO he has lots of chains of command, including direct lines of communication to CINPACFLT and SECNAV, as Modley states.
Yeah, he should have been talking to his boss down the hall, absolutely. In part that should have been happening as part of his job as CO to talk to everyone on his ship from the guy swabbing the deck to his CPOs to his department heads to get ideas and develop plans for dealing with the problem. Sure he is in command and ultimately the buck stops with him, but no competent CO makes it through a day in command without relying on the input and initiative of his trusted subordinates. On a well run ship everyone does his job without being told and fills in where things need filling in without being told.
It's a team like every other effective team.