Category-level object pose estimation aims to predict the 6D pose and size of previously unseen instances from predefined categories, requiring strong generalization across diverse object instances. Although many previous methods attempt to mitigate intra-class variations, they often struggle with instances exhibiting complex geometries or significant deviations from canonical shapes. To address this challenge, we propose INKL-Pose, a novel category-level object pose estimation framework that enables INstance-adaptive Keypoint Learning with local-to-global geometric aggregation. Specifically, our approach first predicts semantically consistent and geometric informative keypoints through an Instance-Adaptive Keypoint Generator, then refines them with: (1) a Local Keypoint Feature Aggregator capturing fine-grained geometries, and (2) a Global Keypoint Feature Aggregator using bidirectional Mamba for structural consistency. To enable bidirectional modeling in Mamba, we introduce a Feature Sequence Flipping strategy that preserves spatial coherence while constructing backward feature sequences. Additionally, we design a surface loss and a separation loss to enforce uniform coverage and spatial diversity in keypoint distribution. The generated keypoints are finally mapped to a canonical space for regressing the object's 6D pose and size. Extensive experiments on CAMERA25, REAL275, and HouseCat6D demonstrate that INKL-Pose achieves state-of-the-art performance and significantly outperforms existing methods.