Alzheimer's disease (AD) is a progressive neurodegenerative disorder that severely impairs cognitive function and quality of life. Timely intervention in AD relies heavily on early and precise diagnosis, which remains challenging due to the complex and subtle structural changes in the brain. Most existing deep learning methods focus only on a single plane of structural magnetic resonance imaging (sMRI) and struggle to accurately capture the complex and nonlinear relationships among pathological regions of the brain, thus limiting their ability to precisely identify atrophic features. To overcome these limitations, we propose an innovative framework, MPF-KANSC, which integrates multi-plane fusion (MPF) for combining features from the coronal, sagittal, and axial planes, and a Kolmogorov-Arnold Network-guided spatial-channel attention mechanism (KANSC) to more effectively learn and represent sMRI atrophy features. Specifically, the proposed model enables parallel feature extraction from multiple anatomical planes, thus capturing more comprehensive structural information. The KANSC attention mechanism further leverages a more flexible and accurate nonlinear function approximation technique, facilitating precise identification and localization of disease-related abnormalities. Experiments on the ADNI dataset confirm that the proposed MPF-KANSC achieves superior performance in AD diagnosis. Moreover, our findings provide new evidence of right-lateralized asymmetry in subcortical structural changes during AD progression, highlighting the model's promising interpretability.