Vertebral compression fractures (VCFs) are a common and potentially serious consequence of osteoporosis. Yet, they often remain undiagnosed. Opportunistic screening, which involves automated analysis of medical imaging data acquired primarily for other purposes, is a cost-effective method to identify undiagnosed VCFs. In high-stakes scenarios like opportunistic medical diagnosis, model interpretability is a key factor for the adoption of AI recommendations. Rule-based methods are inherently explainable and closely align with clinical guidelines, but they are not immediately applicable to high-dimensional data such as CT scans. To address this gap, we introduce a neurosymbolic approach for VCF detection in CT volumes. The proposed model combines deep learning (DL) for vertebral segmentation with a shape-based algorithm (SBA) that analyzes vertebral height distributions in salient anatomical regions. This allows for the definition of a rule set over the height distributions to detect VCFs. Evaluation of VerSe19 dataset shows that our method achieves an accuracy of 96% and a sensitivity of 91% in VCF detection. In comparison, a black box model, DenseNet, achieved an accuracy of 95% and sensitivity of 91% in the same dataset. Our results demonstrate that our intrinsically explainable approach can match or surpass the performance of black box deep neural networks while providing additional insights into why a prediction was made. This transparency can enhance clinician's trust thus, supporting more informed decision-making in VCF diagnosis and treatment planning.