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Large language models (LLMs) increasingly exhibit capabilities that resemble human Learning by Thinking (LbT), the acquisition of new insight through internal processes such as explanation and reasoning, without new external input. A systematic account of the cognitive mechanisms behind these capabilities, and of their limits, remains underdeveloped. This paper proposes a Cognitive LbT Framework that maps four mechanisms (Reflective Reasoning, Synthetic Memory Formation, Internal Simulation, and Conceptual Self-Organization) onto computational processes in LLMs. Drawing on representative methods, including chain-of-thought prompting, self-consistency, self-reflection, Tree-of-Thoughts search, Self-Instruct, and self-taught reasoning, the analysis argues that selected methods can functionally approximate aspects of these mechanisms and can improve performance on some tasks without additional labeled examples, although this does not always constitute durable learning in model parameters. For example, Self-Instruct generated approximately 52,000 instructions from 175 seed tasks and reported a 33% absolute improvement on Super-NaturalInstructions (Y. Wang et al., 2023). The same mechanisms also produce characteristic failures, including hallucination diffusion, model collapse, concept drift, and high computational cost. These failures are not isolated technical defects but follow from four structural asymmetries between LLMs and human cognition: the identity of generator and monitor, closed learning loops without external grounding, symbolic rather than sensorimotor simulation, and the cost of inference-time computation. The framework yields testable propositions about when LbT in LLMs should succeed or fail and offers a structured basis for designing more reliable autonomous learning systems.