Why no shear in "Div, grad, curl, and all that"?

Are there good reasons for the absence of shear and gradients of vectors in the undergraduate curriculum, or have we simply been negligent by not explicitly introducing students to these concepts early on? In this paper, we (i) remind the reader that div and curl are not the entire story when it comes to vector derivatives and (ii) ask the reader to consider whether the missing information-shear or the more general vector gradient-should be included in the undergraduate curriculum. In an attempt to address this last point, we give a list of hypothetical responses to the question "Why no shear?," along with some arguments both for and against teaching it. We leave it to the readers to choose among these reasons or to come up with one of their own when deciding whether or not to include shear and vector gradients in their undergraduate teaching.