Automatic red teaming increasingly relies on large language models (LLMs) to iteratively diagnose failed attacks and propose improved adversarial prompts or injections. Although prior work strengthens this loop through prompt engineering and search-harness design, the mechanisms underlying its two core roles, criticism and attack proposal, has not been explored. To further investigate the core roles and therefore improve red teaming effectiveness, we disentangle two design choices: whether criticism is generated by the target session itself (self-criticism) or by a separately instantiated critic (external criticism), and whether that criticism is translated into the next attack by the target session (self-proposal) or by a separate attacker (external proposal). Through our analysis, we find that self-criticism is more effective because it is grounded in the target's live execution context, including observations, constraints, and available reasoning; removing reasoning reduces downstream attack success by 6%-17%. In contrast, self-proposal is substantially less effective because awareness of the adversarial objective induces explicit refusal and non-refusal sandbagging. These findings motivate a role-separated red-teaming approach: the target session diagnoses why an attack failed, while a separately instantiated attacker generates the next proposal. On DTAP-BENCH, spanning Telecom, Workflow, CRM, and Code domains, under both direct misuse and indirect threat models, as well as multiple agent frameworks, this configuration achieves 63.2% overall attack success rate (ASR), much higher than baselines. Our results show that effective automatic red teaming depends not only on model capability and search strategy, but also on how execution context and adversarial responsibility are distributed across model sessions.

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