The claim that the president does not have to divulge private communications between himself and his advisors is known as

The claim is known as the Executive Privilege.  It is the right of the President of the United States and high-level executive branch officers to keep certain informations private. The claim is based on the doctrine of separation of powers, it means that one government branch does not have the right to ask information into the operations of another, and that the president should be able to acquire private information from his  subordinates.