CNN President Jeff Zucker stood by Chris Cuomo last spring after revelations that the star anchor had helped his brother, former New York Gov. Andrew Cuomo, navigate a sexual-harassment scandal.

In a virtual town hall with staffers in May, he conceded that Chris Cuomo had “made a mistake,” but also said he wasn’t surprised that the anchor discussed the matter with his brother. Mr. Zucker said suspending Chris Cuomo would be “punishment for the sake of punishing.”