One debate among business owners and policymakers centres on whether higher education institutions (HEIs) have failed to transform the younger generation by developing their competencies, skills, values and behaviours to enable them to be fit for the world of work. While previous studies have considered the importance of skills development and its assessment in many contexts, there appears to have been limited scholarly research on employability issues within the higher education system (HES) in Nigeria. In seeking to address this, it is vital to understand how HEIs in Nigeria conceptualize generic skills and why HEIs have problems with teaching generic skills in their programmes. By adopting a qualitative approach, based on interviews with senior academics, industry executives and final-year undergraduates, this study found that many of the HEIs do not facilitate the teaching of high-level generic skills in their programmes. Some of the factors attributed to this include poor learning environment, lack of staff with industry experience, and over-dependence on theoretical content teaching. The findings are significant for reorienting the HE curriculum developers to align with the needs of the industry and society. Regarding implications for policy, we recommend that enterprise education be made mandatory for primary, secondary and tertiary education curriculum in Nigeria. Finally, we advocate more inclusive and interpretive research for greater understanding of the issues, and to offer useful data for policymaking and decision-making on the perspectives of preparing graduates for work.