How do people come to opposite causal judgments about societal problems, such as whether a public health policy reduced COVID-19 cases? The current research tests an understudied cognitive mechanism in which people may agree about what "actually" happened (e.g., that a public health policy was implemented and COVID-19 cases declined), but can be made to disagree about the counterfactual, or what "would have" happened otherwise (e.g., whether COVID-19 cases would have declined naturally without intervention) via comparison cases. Across two preregistered studies (total N = 480), participants reasoned about the implementation of a public policy that was followed by an immediate decline in novel virus cases. Study 1 shows that people's judgments about the causal impact of the policy could be pushed in opposite directions by emphasizing comparison cases that imply different counterfactual outcomes. Study 2 finds that people recognize they can use such information to influence others. Specifically, in service of persuading others to support or reject a public health policy, people systematically showed comparison cases implying the counterfactual outcome that aligned with their position. These findings were robust across samples of U.S. college students and politically and socioeconomically diverse U.S. adults. Together, these studies suggest that implied counterfactuals are a powerful tool that individuals can use to manufacture others' causal judgments and warrant further investigation as a mechanism contributing to belief polarization.