The new European “Farm to Fork” Strategy has been praised for addressing the issue of the long‐run sustainability of the food system. In this document, the link between human and planetary health is often recalled. However, consumers' aspiration to healthy food is dealt with only superficially. This article analyzes and challenges the position assumed by the European Commission on this topic, using a holistic and transdisciplinary approach to food, called pantrophy. Drawing on several disciplines beyond food science and economics, the author argues that health is not only a question of diet. As a social fact, healthy food is a blend of moral dilemma, a luxury, a fashion item, an object of desire, and a sign of distinction. Therefore, it will hardly become cheap and easily available, as suggested by the Strategy. For the same reason, even the market mechanism envisaged to spread healthier eating habits might prove ineffective. The author calls for a radical change of the European policy in order to ensure that access to healthy food does not become unjust, discriminatory, and a cause of social conflict. The challenge consists in shifting part of the governmental institutions' effort from changing consumption styles to guaranteeing the intrinsic quality of food at its source.