The antonym for the phrase "breaking a story" would be "suppressing a story." Breaking a story means to reveal or make public new information, especially news, to the public. On the other hand, suppressing a story means to prevent or stop a story from being made public or known. Keeping information from the public can occur for various reasons, such as legal implications, corporate interests, or privacy concerns. In journalism, suppressing a story without a compelling reason can be considered unethical and might lead to accusations of bias or censorship.