Sexgender has become politicized by neo-conservative and populist movements in Europe and elsewhere. This article explores how the sexgender binary is foundational to the social and material construction of the non-heterosexual legal subject and unveils binary hierarchies embedded therein. Furthermore, it develops a new materialist methodology called BinaryTech, which exposes the binary formulas of inequality and difference in the Court’s jurisprudence. This new materialist approach, based on Karen Barad’s agential realism, is used to critically examine how differences are produced as stable features of subjects and objects. The human of the Convention being heterosexual is thereby the result, constructed on material-discursive differentiation of non-heterosexuals. The article concludes by describing how new materialist interventions and Nordic feminist perspectives on law can offer valuable insights within the emerging material turn.