It surprises me that people don’t understand what going up the chain of command entails. If you have an issue and your immediate superior is unable to effectively deal with it, then you have the right to go above that person’s head.
If the next immediate superior is unable to deal with the situation, then you have the right to go above that person’s head, and so on all the way up the chain of command.
I don’t know what steps Captain Crozier took, but he obviously felt that this was insufficient and that he was dealing with an emergency situation and didn’t have time to go through the normal channels.
From the Navy’s perspective, he went outside standard operating procedures. That is all they need to justify firing him.
However in the military, they are taught that it is illegal to obey an illegal order. If obeying an order or in this case “standard operating procedures” means injury or death to a service member then one has an obligation to disregard such order.
Captain Crozier did the right thing.