The path to higher network autonomy in 6G lies beyond the mere optimization of key performance indicators (KPIs), requiring systems that perceive and reason over the network environment as it is. This can be achieved through agentic AI, where large language model (LLM)-powered agents utilize multimodal telemetry, memory, and cross-domain negotiation to achieve multi-objective goals. However, deploying such agents introduces cognitive biases inherited from human design, which can severely distort reasoning and actuation. This paper provides a comprehensive tutorial on well-known cognitive biases, detailing their taxonomy, mathematical formulation, emergence in telecom systems, and tailored mitigation strategies. We validate these concepts through two distinct use-cases in 6G management. First, we tackle anchoring bias in inter-slice resource negotiation. To overcome the prohibitive execution delays of cloud-based LLMs, this use-case deploys a locally hosted 1B-parameter model on an RTX A4000 GPU, successfully achieving sub-second inference latencies compatible with near-real-time operations. By replacing fixed heuristic anchors with a Truncated Weibull randomized anchor strategy, the agents dismantle rigid biases, intelligently consume SLA slack, and dynamically double the system-wide energy savings (peaking at 25\%) without violating strict latency limits. Second, we mitigate temporal and confirmation biases in RAN-Edge cross-domain negotiation by designing an unbiased collective memory. By integrating semantic/temporal decay and an inflection bonus that actively highlights past negotiation failures, agents are prevented from over-relying on recent data or repeating past mistakes. Grounding decisions in this richer, debiased historical context yields highly robust agreements, achieving a $\times 5$ latency reduction and roughly 40\% higher energy savings compared to memoryless baselines.