The CEO of a publicly traded company has a legal obligation to disclose any matter that can impact the stockprice positively or negatively. This certainly falls in that category.
Also, for better or worse, part of being a public figure is living with the fact that your wellbeing impacts a lot of people, and these people have a right to know what that impact will be.
If he resigned he should have absolutely privacy, but since he hasn't the thousands of people that rely on him have a right to know where they stand.
He really has no such obligation. Do you have any idea how many things a CEO knows that might negatively impact the share price of an organisation?
He has the obligation to release certain specific information mandated by the SEC in a timely manner (details of his health are not on the list - it's largely financial) and there are certain things a company can not say (which basically boils down to honesty).
The SEC also say he and the company have to communicate in a particular way when information is shared (for instance so it's available to the whole market - no selective disclosure, and again it has to be honest and truthful and so on) and projections are heavily caveated.
The on top of that he has a general legal obligation to act in the best interests of share holders.
But there's no blanket reveal all, and nothing that specifically covers his health and I'm not sure why you think there is or where it comes from. Could you quote the specific authority or law in question?
No - the CEO has a legal obligation clearly spelled out by the SEC and other laws, I'm sure.
Given that the market is made up of humans, and that nobody can predict with certainty the public reaction to every move a company or person makes, it's absurd to think that insiders in a corporation are not entitled to privacy.
Also, for better or worse, part of being a public figure is living with the fact that your wellbeing impacts a lot of people, and these people have a right to know what that impact will be.
If he resigned he should have absolutely privacy, but since he hasn't the thousands of people that rely on him have a right to know where they stand.