On Tuesday, in a fifty-eight-second video posted on X, Robert F. Kennedy, Jr., the Secretary of Health and Human Services, made a remarkable announcement: under his watch, he said, the Centers for Disease Control and Prevention would no longer advise healthy children and pregnant women to get vaccinated against COVID-19. For decades, the C.D.C. has based its vaccination policy in large part on the recommendations of a panel of experts, who carefully review data about vaccine safety and effectiveness.