Semantic correspondence (SC) aims to establish semantically meaningful matches across different instances of an object category. We illustrate how recent supervised SC methods remain limited in their ability to generalize beyond sparsely annotated training keypoints, effectively acting as keypoint detectors. To address this, we propose a novel approach for learning dense correspondences by lifting 2D keypoints into a canonical 3D space using monocular depth estimation. Our method constructs a continuous canonical manifold that captures object geometry without requiring explicit 3D supervision or camera annotations. Additionally, we introduce SPair-U, an extension of SPair-71k with novel keypoint annotations, to better assess generalization. Experiments not only demonstrate that our model significantly outperforms supervised baselines on unseen keypoints, highlighting its effectiveness in learning robust correspondences, but that unsupervised baselines outperform supervised counterparts when generalized across different datasets.