The "reasoning" text that we see is what the model learned during the post training. In the post training datasets of reasoning models, "reasoning" is fed to the model with inputs and outputs. So the model learns - X is Y because the given "reasoning" text. This happens millions of times during the post training and that's how the model generalizes "reasoning". This is how the models learn anything; and the AI companies taught the models reasoning as well - they didn't have to; they could have just trained the model on input and output (X is Y); the model would have learned the exact same relationships.