Zero-shot anomaly detection aims to identify defects in unseen categories without target-specific training. Existing methods usually apply the same feature transformation to all samples, treating normal and anomalous data uniformly despite their fundamentally asymmetric distributions, compact normals versus diverse anomalies. We instead exploit this natural asymmetry by proposing AVA-DINO, an anomaly-aware vision-language adaptation framework with dual specialized branches for normal and anomalous patterns that adapt frozen DINOv3 visual features. During training on auxiliary data, the two branches are learned jointly with a text-guided routing mechanism and explicit routing regularization that encourages branch specialization. At test time, only the input image and fixed, predefined language descriptions are used to dynamically combine the two branches, enabling an asymmetric activation. This design prevents degenerate uniform routing and allows context-specific feature transformations. Experiments across nine industrial and medical benchmarks demonstrate state-of-the-art performance, achieving 93.5% image-AUROC on MVTec-AD and strong cross-domain generalization to medical imaging without domain-specific fine-tuning. https://github.com/aqeeelmirza/AVA-DINO