There has been an intense focus on the '21st century skills' and on universities developing graduate attributes through teaching, learning and innovative curricula. One example is resilience, frequently cited as desirable, especially during and post the COVID-19 pandemic. Resilience gained momentum across a number of fields, such as development studies, ecology and education, examining the ability of people, institutions, environments, and societies to 'bounce back' from crisis or adversity. Despite its popularity, however, resilience has no shared meaning, with scholars emphasising the looseness, potential vacuousness, and lack of ideological clarity of the concept (van Breda, 2018; Brewer et al., 2019; Zembylas, 2021). This paper examines resilience with specific reference to higher education and interrogates its deployment as a graduate attribute with respect to individual students and higher education curricula. It will be argued that tensions inherent in the South African system are brought to the fore, particularly in the context of current debates on the relevance of resilience for the complexity and change anticipated in the 21st century. The resulting ambiguity burdens universities, which requires courageousness in the quest for accessibility and self-awareness of precarity as an operational feature (Barnett, 2000: 409). It is argued that universities are trapped by supercomplexity on the one hand, with its "multiplicity of frameworks" and competing demands (Barnett, 2000: 415) and, on the other hand, access to resources and state regulatory and policy requirements. Furthermore, apartheid-defined realities continue to define the present, rendering the future more complex. The rhetoric in South African higher education policy imbues universities with an apparent superpower: to produce graduates with a (continuously shifting and increasing) set of attributes. The development of attributes is a complex process and is dependent and contingent on multiple variables. Among these are the contexts and histories of individual students, which define whether and to what extent graduate attributes are achieved, and a set of outcomes that can neither be determined nor guaranteed. Through the lens of resilience, the paper interrogates whether the development of graduate attributes can be solely the university's task and whether this expectation is justified both in the absence of consideration of students' agency and in the complex worlds outside the university.