That article is silly. The defense secretary cannot arbitrarily fire people like this. He can have a 15-6 investigation opened though, but that is a long way from a firing. To arbitrarily fire an officer there has to be some immediate violation of law or gross harm with exigencies.

Where these immediate firings occur for senior officers is typically a failure of performance in a command position that results in some other greater failure, but this is beyond rare, even in combat.

Unfortunately, "can't" and "illegal" and even "unconstitutional" are really only nuisance words to today's government.