Automated program repair (APR) has shown promising results, particularly with the use of neural networks. Currently, most APR tools focus on code transformations specified by test suites, rather than reasoning about the program intent and the high-level bug specification. Without a proper understanding of program intent, these tools tend to generate patches that overfit incomplete test suites and fail to reflect the developers intentions. However, reasoning about program intent is challenging. In our work, we propose an approach called AdverIntent-Agent, based on critique and adversarial reasoning. Our approach is novel to shift the focus from generating multiple APR patches to inferring multiple potential program intents. Ideally, we aim to infer intents that are, to some extent, adversarial to each other, maximizing the probability that at least one aligns closely with the developers original intent. AdverIntent-Agent is a multi-agent approach consisting of three agents: a reasoning agent, a test agent, and a repair agent. First, the reasoning agent generates adversarial program intents along with the corresponding faulty statements. Next, the test agent produces adversarial test cases that align with each inferred intent, constructing oracles that use the same inputs but have different expected outputs. Finally, the repair agent uses dynamic and precise LLM prompts to generate patches that satisfy both the inferred program intent and the generated tests. AdverIntent-Agent was evaluated on two benchmarks: Defects4J 2.0 and HumanEval-Java. AdverIntent-Agent correctly repaired 77 and 105 bugs in both benchmarks, respectively.