It roughly works by piecing together sentences based on the probability of the various elements (mainly words but also more complex) being there in various relations to each other, the “probability curves” (not quite probability curves but that’s a good enough analog) having been derived from the very large language training sets used to train them (hence LLM - Large Language Model).
This is why you might get things like pieces of argumentation which are internally consistent (or merelly familiar segments from actual human posts were people are making an argument) but they’re not consistent with each other - the thing is not building an argument following a logic thread, it’s just putting together language tokens in common ways which in its training set were found associate with each other and with language token structures similar to those in your question.