President Nixon's claim that he had the right to protect private conversations lead to a conflict over executive privilege.
Executive privilege is a concept that can prevent the president from sharing information with the American public. This privilege is usually only used if the issue at hand is a matter of national security. In this case, Nixon was using it to prevent the courts from getting recorded conversations between Nixon and other people.
This claim was not supported by the Supreme Court. In the case US vs. Nixon, the Supreme Court unanimously voted that Nixon must hand over the tapes because "no one is above the law."
