An interdisciplinary approach involving linguistics, rhetoric, and argumentation theory helps reveal how people argue their opinions and decisions. Although the pandemic is a common experience, its risks are perceived in different ways. For some, the real threat is Covid-19 and the remedy is vaccination. For others, however, the real risk is the vaccine and the “remedy” is refusal to get vaccinated. Justifying their opinions on the subject, Italian Internet users refer to common values (such as life, health, responsibility, etc.). However, since Internet users diagnose risks in different ways, they make use of shared values in differing ways. In this paper, the views of those for and against vaccination are analyzed from three complementary perspectives. The first one concerns the differences in which people conceive of various values. The second one shows how, using the same topoi, pro- and anti-vaccine advocates create different hierarchies of values that are fundamental to their respective decisions. Finally, the third one explores differences in the ways values are used in various argumentation schemes used in disputes on vaccination.