Large language models (LLMs) have shown promise in automated unit test generation, yet achieving high branch coverage for complex methods remains challenging. We attribute this limitation not to model capability alone, but to a fundamental cognitive misalignment between what LLM prompts expose and what branch reachability requires: implicit cross-method preconditions are hidden, while branch-irrelevant code is over-provided. To address this misalignment, we propose CogPath, a unit test generation framework that externalizes hidden path conditions as Constraint-Hints and isolates branch-relevant dependencies via coverage-driven Backward Slicing, within an iterative generate-execute-repair loop. Our empirical evaluation, conducted on 2971 methods with cyclomatic complexity greater than 10 from 14 open-source projects, demonstrates that CogPath achieves 12.8% higher line coverage and 10.2% higher branch coverage compared to the state-of-the-art, with improvements reaching 32.3% and 20% respectively on the most complex project.