While self-supervised learning has improved anomaly detection in computer vision and natural language processing, it is unclear whether tabular data can benefit from it. This paper explores the limitations of self-supervision for tabular anomaly detection. We conduct several experiments spanning various pretext tasks on 26 benchmark datasets to understand why this is the case. Our results confirm representations derived from self-supervision do not improve tabular anomaly detection performance compared to using the raw representations of the data. We show this is due to neural networks introducing irrelevant features, which reduces the effectiveness of anomaly detectors. However, we demonstrate that using a subspace of the neural network's representation can recover performance.