Denmark is a generous welfare state which provides resources and legal means for fathers to take their parental role seriously and engage with their children. In this paper, we explore the relation between Danish fathers' interaction online and the societal, legal, and economic infrastructures in which they are situated. By focusing on how fathers living in Denmark make use of the Internet and social media sites to facilitate their role as parents, we are able to explore how online engagement is shaped by the different societal 'norms' of parenting. Our research outlines the ways in which societal infrastructures influence how fathers perceive, and subsequently make use of social media in relation to child-caring. We find that fathers discuss their experiences of legal inequities and stereotypical discrimination on social network sites like Facebook. We also study fathers' online reviews of a Danish parenting App, FAR, designed specifically to support fathers. By analyzing social media discussions around fatherhood in Denmark, we found connections to the ways in which the current political climate shapes and influences fatherhood in Denmark, as they reflect the societal infrastructures which situate fathers in contemporary Denmark. Further, we found a strong political interest for collective action to transform the societal infrastructures to support legal equality for child caretaking across genders. This strong political motivation is distinct from existing studies exploring how fatherhood is displayed on social media in other countries such as the USA. On this basis, we argue that research exploring social media use in institutions which are strongly shaped by societal norms, must explicitly consider the role which society takes in shaping such institutions, and include these aspects into the analysis. Our data show that fathers use social media sites as platforms to produce a fatherhood more in line with their lived experience of parenting, and that they advocate for collective political action to strengthen fathers' legal rights. Copyright is held by the owner/author(s). Publication rights licensed to ACM.