No, it doesn't. It reaches the conclusion because of vector similarity (simplified explanation): these explanations are post-hoc.
The best available evidence suggests this is also true of any explanations a human gives for their own behaviour; nevertheless we generally accept those at face value.
GPT-based predictive text systems are incapable of introspection of any kind: they cannot execute the algorithm I execute when I'm giving explanations for my behaviour, nor can they execute any algorithm that might actually result in the explanations becoming or approaching truthfulness.
The GPT model is describing a fictional character named ChatGPT, and telling you why ChatGPT thinks a certain thing. ChatGPT-the-character is not the GPT model. The GPT model has no conception of itself, and cannot ever possibly develop a conception of itself (except through philosophical inquiry, which the system is incapable of for different reasons).
If an LLM is told to do reasoning and then state the answer, it follows that the answer is basically guaranteed to be derived from the previously generated reasoning.
Video series on the topic: https://www.3blue1brown.com/topics/neural-networks
Which is to say that “why” it gives those answers is because its statistically likely within its training data that when there are the words, “why did you connect line and log with paper” the text which follows could be “logs are made of wood and lines are in paper.” But that is not the specific relation of the 3 words in the model itself, which is just a complex vector space.