Recent advancements in Large Language Models (LLMs) have successfully employed search-based strategies to enhance code generation. However, existing methods typically rely on static, sparse public test cases for verification, leading to pseudo-correctness -- where solutions overfit the visible public tests but fail to generalize to hidden test cases. We argue that optimizing against a fixed, weak environment inherently limits robustness. To address this, we propose AdverMCTS, a novel adversarial Monte Carlo Tree Search framework that combats pseudo-correctness by coupling code search with active vulnerability discovery. AdverMCTS formulates generation as a minimax-style game between a Solver agent, which synthesizes code candidates, and an Attacker agent, which evolves to generate targeted corner test cases that exploit logical divergences in the current code pool. These discovered tests form a dynamic, progressively hostile filter that penalizes fragile reasoning. Extensive experiments demonstrate that AdverMCTS significantly outperforms state-of-the-art baselines, effectively reducing false positive rates and forcing the model to generalize beyond the initial constraints. The resources of this work are available at https://anonymous.4open.science/r/AdverMCTS_open-A255.