Audio deepfakes pose a significant security threat, yet current state-of-the-art (SOTA) detection systems do not generalize well to realistic in-the-wild deepfakes. We introduce a novel \textbf{I}n-\textbf{C}ontext \textbf{L}earning paradigm with comparison-guidance for \textbf{A}udio \textbf{D}eepfake detection (\textbf{ICLAD}). The framework enables the use of audio language models (ALMs) for training-free generalization to unseen deepfakes and provides textual rationales on the detection outcome. At the core of ICLAD is a pairwise comparative reasoning strategy that guides the ALM to discover and filter hallucinations and deepfake-irrelevant acoustic attributes. The ALM works alongside a specialized deepfake detector, whereby a routing mechanism feeds out-of-distribution samples to the ALM. On in-the-wild datasets, ICLAD improves macro F1 over the specialized detector, with up to $2\times$ relative improvement. Further analysis demonstrates the flexibility of ICLAD and its potential for deployment on recent open-source ALMs.