Executively privileging what?

What does “executive privilege” protect?

Here’s Mr Bush: “If the staff of a President operated in constant fear of being hauled before various committees to discuss internal deliberations, the President would not receive candid advice, and the American people would be ill-served…. I'm worried about precedents that would make it difficult for somebody to walk into the Oval Office and say, Mr. President, here's what's on my mind. And if you haul somebody up in front of Congress and put them in oath and all the klieg lights and all the questioning, to me, it makes it very difficult for a President to get good advice.”

Putting aside the melodramatic “constant fear,” “hauled,” and “klieg lights,” what do we have?

Let’s say Mr X gets a call from the president asking him to come into the Oval Office to say what’s on his mind on a particular issue. Mr X says, well, I’d like to tell you what I think, but because I might have to repeat my opinions publicly and state under oath that I’m not lying about what I’ve said to you, I’d rather say nothing.

Now, what kind of honestly held opinion could Mr X possibly have that would be so damaging to him on its being made public that he would rather remain silent than help the president of the United States with an issue Mr X presumably feels strongly about? And how ill served would the American people be by Mr X’s refusal to give such advice? The argument is clearly nonsensical.