<p>Large language models (LLMs) are increasingly deployed in high-stakes applications where reliable confidence estimation is crucial for trustworthy artificial intelligence (AI). However, their confidence dynamics remain poorly understood, with users reporting paradoxical behaviours: LLMs exhibit reduced flexibility in updating initial responses while simultaneously showing excessive sensitivity to contradictory feedback. Understanding these confidence patterns is essential for developing more reliable AI systems and improving human–AI interaction. Here we show that LLM confidence is governed by two competing mechanisms that explain this paradox. First, we identify a choice-supportive bias: when LLMs view their initial answers, they exhibit inflated confidence and maintain their original responses at rates exceeding optimal decision-making, even when presented with contrary evidence. Second, we demonstrate systematic overweighting of contradictory information: LLMs update their confidence more strongly in response to opposing advice than supporting advice, deviating markedly from optimal Bayesian reasoning. These mechanisms operate across diverse models and generalize from simple factual queries to reasoning tasks. Our computational modelling reveals that these two principles—self-consistency preservation and hypersensitivity to contradiction—capture LLM behaviour across domains. These findings provide an understanding of when and why LLMs exhibit adherence to initial responses versus disproportionate updating, with implications for enhancing the robustness and transparency of LLM decision-making.</p>