Multimodal large language models (MLLMs) have recently demonstrated remarkable reasoning and perceptual abilities for anomaly detection. However, most approaches remain confined to image-level anomaly detection and textual reasoning, while pixel-level localization still relies on external vision modules and dense annotations. In this work, we activate the intrinsic reasoning potential of MLLMs to perform anomaly detection, pixel-level localization, and interpretable reasoning solely from image-level supervision, without any auxiliary components or pixel-wise labels. Specifically, we propose Reasoning-Driven Anomaly Localization (ReAL), which extracts anomaly-related tokens from the autoregressive reasoning process and aggregates their attention responses to produce pixel-level anomaly maps. We further introduce a Consistency-Guided Reasoning Optimization (CGRO) module that leverages reinforcement learning to align reasoning tokens with visual attentions, resulting in more coherent reasoning and accurate anomaly localization. Extensive experiments on four public benchmarks demonstrate that our method significantly improves anomaly detection, localization, and interpretability. Remarkably, despite relying solely on image-level supervision, our approach achieves performance competitive with MLLM-based methods trained under dense pixel-level supervision. Code is available at https://github.com/YizhouJin313/ReADL.