In the wake of the COVID-pandemic, and from the perspective of analytical philosophy of education, this paper investigates into, and discusses, costs and benefits to online teaching in higher education. Contrasting old and new ways of teaching, notions that are developed below, notable results in the paper are the following: a) even if expedient, online teaching does not cater well to the situationally contingent dialectical processes that teaching consists in, and, hence, b) it might have unwanted (and detrimental) effects as regards the development of our students' ability to think. Two explanatory principles as regards teaching and learning are stipulated and analysed in the paper: "the teaching trinity" and "the learning staircase." These analyses represent the papers main contribution to knowledge. But also, arguments addressing the importance of the human face in teaching situations, and arguments addressing the "immediacy" characteristic of such situations, represents novel contributions. On the background of said analyses, it is argued that online teaching might have a micro-level marketisation of education as an unintended consequence (the marketisation of teaching), and that this out-crowds important values that teaching traditionally installed. Drawing upon Alan Fiske and Michael Sandel, a frame for understanding this is suggested.