Unsupervised deformable image registration requires aligning complex anatomical structures without reference labels, making interpretability and reliability critical. Existing deep learning methods achieve considerable accuracy but often lack transparency, leading to error drift and reduced clinical trust. We propose a novel Multi-Hop Visual Chain of Reasoning (VCoR) framework that reformulates registration as a progressive reasoning process. Inspired by the iterative nature of clinical decision-making, each visual reasoning hop integrates a Localized Spatial Refinement (LSR) module to enrich feature representations and a Cross-Reference Attention (CRA) mechanism that leads the iterative refinement process, preserving anatomical consistency. This multi-hop strategy enables robust handling of large deformations and produces a transparent sequence of intermediate predictions with a theoretical bound. Beyond accuracy, our framework offers built-in interpretability by estimating uncertainty via the stability and convergence of deformation fields across hops. Extensive evaluations on two challenging public datasets, DIR-Lab 4D CT (lung) and IXI T1-weighted MRI (brain), demonstrate that VCoR achieves competitive registration accuracy while offering rich intermediate visualizations and confidence measures. By embedding an implicit visual reasoning paradigm, we present an interpretable, reliable, and clinically viable unsupervised medical image registration.