The path to higher network autonomy in 6G lies beyond the mere optimization of key performance indicators (KPIs). While KPIs have enabled automation gains under TM Forum Levels 1--3, they remain numerical abstractions that act only as proxies for the real essence of communication networks: seamless connectivity, fairness, adaptability, and resilience. True autonomy requires perceiving and reasoning over the network environment as it is. Such progress can be achieved through \emph{agentic AI}, where large language model (LLM)-powered agents perceive multimodal telemetry, reason with memory, negotiate across domains, and act via APIs to achieve multi-objective goals. However, deploying such agents introduces the challenge of cognitive biases inherited from human design, which can distort reasoning, negotiation, tool use, and actuation. Between neuroscience and AI, this paper provides a tutorial on a selection of well-known biases, including their taxonomy, definition, mathematical formulation, emergence in telecom systems and the commonly impacted agentic components. The tutorial also presents various mitigation strategies tailored to each type of bias. The article finally provides two practical use-cases, which tackle the emergence, impact and mitigation gain of some famous biases in 6G inter-slice and cross-domain management. In particular, anchor randomization, temporal decay and inflection bonus techniques are introduced to specifically address anchoring, temporal and confirmation biases. This avoids that agents stick to the initial high resource allocation proposal or decisions that are recent and/or confirming a prior hypothesis. By grounding decisions in a richer and fairer set of past experiences, the quality and bravery of the agentic agreements in the second use-case, for instance, are leading to $\times 5$ lower latency and around $40\%$ higher energy saving.

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