The role of higher education (HE) in the development of societies is an unquestionable fact, and its management has traditionally been a major concern of governments. Lately, there has been worldwide debate on whether universities should adopt traditional management practices as applied in any business sector. This paper questions the adoption of these practices, because they tend to simplify the complexity of this service, and argues that service-dominant logic (SDL) is a more appropriate approach to manage HE institutions. It envisions HE as a complex system where many actors interact to co-create value and focuses on the student-teacher dyad. Through a critical literature review, this paper states that the increasing established analogy of the 'student-customer' and 'teacher-provider', adopted to simplify the complexity of the HE service and thus allow the implementation of traditional management practices, jeopardizes the sustainability of social development due to its effects on the long-term quality of professionals' training. Then, under the frame of SDL, we define students as co-creators of value (rather than customers) and teachers as value proposers, providing new insights to the debate and critical new recommendations for policymakers and universities to manage this critical relationship.