LLMs are trained to see parts of a document and reproduce the other parts, that's why they are called "language models".
For example, they might learn that the words "strawberries are" are often followed by the words "delicious", "red", or "fruits", but never by the words "airplanes", "bottles" or "are".
Likewise, they learn to mimic reasoning contained in their training data. They learn the words and structures involved in an argument, but they also learn the conclusions they should arrive at. If the training dataset consists of 80 documents arguing for something, and 20 arguing against it (assuming nothing else differentiates those documents (like length etc.)), the LLM will adopt the standpoint of the 80 documents, and argue for that thing. If those 80 documents contain flawed logic, so will the LLM's reasoning.
Of course, you could train a LLM on a carefully curated selection of only documents without any logical fallacies. Perhaps, such a model might be capable of actual logical reasoning (though it would still be biased by the conclusions contained in the training dataset)
But to train an LLM you need vasts amount of data. Filtering out documents containing flawed logic does not only require a lot of effort, it also reduces the size of the training dataset.
Of course, that is exactly what the big companies are currently researching and I am confident that LLMs will only get better over time, but the LLMs of today are trained on large datasets rather than perfect ones, and their architecture and training prioritize language modelling, not logical reasoning.