One of the things I point out to my students frequently is that business is a collaborative activity, and collaboration requires that we agree on objectives and methods. That can mean convincing your team-mates, your subordinates, or even your boss of the best course of action. That means you need to understand the mechanics of using argumentation and how to use it effectively for persuasion. That, in turn, requires critical thinking.
With regard to bosses, see this useful piece from Harvard Business Review: Getting the Boss to Buy In
It focuses on the notion of “issue selling” — in particular, selling your boss on a new idea.
Issue sellers who accomplish their goals, we found, look for the best ways, venues, and times to voice their ideas and concerns—using rhetorical skill, political sensitivity, and interpersonal connections to move the right leaders to action….
The article isn’t cast in terms of critical thinking, but the connection is there. Students of critical thinking should read this article and ask which of Susan Ashford and James Detert’s bits of advice require the application of the core skills of critical thinking.