Storing sensitive communications and data on a private server is practically asking for a foreign government or hacker to try and compromise it. Especially when the information belongs to a U.S. Cabinet Secretary, the use of private servers is too risky for national security.
If Cabinet Secretaries have a legitimate reason for wanting to use a private server for official government business, they should be able to, if they can prove the server is secure. They can be trusted to preserve classified information from those trying to access it.