Availability attacks, which poison the training data with imperceptible perturbations, can make the data \emph{not exploitable} by machine learning algorithms so as to prevent unauthorized use of data. In this work, we investigate why these perturbations work in principle. We are the first to unveil an important population property of the perturbations of these attacks: they are almost \textbf{linearly separable} when assigned with the target labels of the corresponding samples, which hence can work as \emph{shortcuts} for the learning objective. We further verify that linear separability is indeed the workhorse for availability attacks. We synthesize linearly-separable perturbations as attacks and show that they are as powerful as the deliberately crafted attacks. Moreover, such synthetic perturbations are much easier to generate. For example, previous attacks need dozens of hours to generate perturbations for ImageNet while our algorithm only needs several seconds. Our finding also suggests that the \emph{shortcut learning} is more widely present than previously believed as deep models would rely on shortcuts even if they are of an imperceptible scale and mixed together with the normal features. Our source code is published at \url{https://github.com/dayu11/Availability-Attacks-Create-Shortcuts}.