Knowledge distillation has become a prevalent technique for deploying efficient recommender systems, enabling lightweight student models to approximate the performance of larger teachers. However, we identify a critical issue: distillation systematically amplifies popularity bias, as student models inherit and intensify the popularity-driven shortcuts encoded in teachers trained on interaction data dominated by popular items. To address this limitation, we propose GUIDE (Geodesic aware Unbiased Instructive Distillation with Experts), a collaborative distillation framework that incorporates domain-specific debiasing experts alongside the global teacher. GUIDE tackles two key challenges in this paradigm. First, for expert routing, we introduce Spherical Expert Alignment, which conducts expert-student matching on the spherical manifold with geodesic distance optimization, eliminating magnitude-induced bias and ensuring stable gradient flow. Second, for context fusion, we design a Meta-Debiasing Gate that dynamically arbitrates teacher-expert influence based on real-time user-item context through end-to-end meta-learning. Extensive experiments on multiple real-world datasets demonstrate that GUIDE significantly mitigates popularity bias while preserving recommendation accuracy, with state-of-the-art trade-offs among efficiency, accuracy, and fairness. The code and data are available at:https://github.29com/zx19971219/GUIDE.