Standard accuracy benchmarks evaluate whether large language models (LLMs) reach correct answers. However, they do not test whether models maintain that answer when challenged by a plausible counter-argument. We introduce a controlled protocol for evaluating answer stability: after a model answers a multiple-choice question correctly, we challenge the model's answer with a coherent argument for an incorrect option and measure whether the model flips. The setup a) isolates argumentative content from overt social pressure and b) varies argument length, self-attribution, and cross-model source. Across seven frontier models and 57 MMLU subjects, flip rates range from 17.5% to 97.3%, revealing large differences in stability that are not captured by accuracy metrics alone. We find that self-attribution consistently increases flip rates (mean 7.1pp, up to 18.7pp). Furthermore, pooling wrong-answer arguments across models and selecting the most effective one per question yields stronger adversarial challenges than relying on any single source model. From this cross-model pool, we construct MaxFlip, a curated benchmark that amplifies answer flips by up to 23.6pp over self-generated challenges. We release the protocol, challenge records, and MaxFlip to support stability evaluation alongside standard accuracy benchmarks. Materials are available at https://github.com/nafisenik/WhoFlips, https://hf.co/datasets/nafisehNik/WhoFlips.

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