While debate continues about how to define and measure employability, most accounts revolve around a deceptively simple idea--whether or not a person obtains a job depends on their acquiring certain skills and attributes in college that are desired by employers in the labor market. The narrative advanced by this perspective raises two critical questions that are increasingly pressing for postsecondary leaders: (1) How can colleges and universities cultivate employability in their students? and (2) How can institutions measure and prove their students' employability to policy makers and taxpayers? To answer these questions, it is essential to recognize growing critiques in countries such as Australia and England about the notion of employability itself (Clarke, 2018; Moreau & Leathwood, 2006). In a new course in the Department of Educational Policy Studies at the University of Wisconsin-Madison (UW-Madison), the authors examined these questions and critiques over 16 weeks of intense reading, discussion, and debate. This article is a product of that semester of debate about employability and its impact on U.S. higher education. Ultimately, the authors contend that too many institutions and advocates of employability are unquestioningly (and perhaps unwittingly) adopting a market-based discourse of skills and education that contradicts long-held values associated with higher education and its role in society.