One debate among business owners and policymakers' centre on whether higher education institutions (HEIs) are failing to transform the young generation by reorienting education to develop higher competencies, skills, values and behaviours. 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 its graduate programmes. By adopting a qualitative approach, based on interviews with senior academics, industry executives and final year undergraduates, this study finds that many of 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 re-orienting HE curriculum to align with the needs of the industry and society. Regarding, implications for policy, we recommend that enterprise education be mandatory in the curriculum for primary, secondary and tertiary education in Nigeria. Finally, we advocate more inclusive and interpretive research for greater understanding of the issues to offer useful data for policymaking and decision-making on the perspectives of preparing graduates for work.