Deep learning has shown significant potential in diagnosing neurodegenerative diseases from MRI data. However, most existing methods rely heavily on large volumes of labeled data and often yield representations that lack interpretability. To address both challenges, we propose a novel self-supervised cross-encoder framework that leverages the temporal continuity in longitudinal MRI scans for supervision. This framework disentangles learned representations into two components: a static representation, constrained by contrastive learning, which captures stable anatomical features; and a dynamic representation, guided by input-gradient regularization, which reflects temporal changes and can be effectively fine-tuned for downstream classification tasks. Experimental results on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset demonstrate that our method achieves superior classification accuracy and improved interpretability. Furthermore, the learned representations exhibit strong zero-shot generalization on the Open Access Series of Imaging Studies (OASIS) dataset and cross-task generalization on the Parkinson Progression Marker Initiative (PPMI) dataset. The code for the proposed method will be made publicly available.