There is no mysticism behind the curtains, just computer science + math.
We can’t explain it because we distilled so many inputs into matrixes and transformed them over and over again. If we had all the time and computing power in the universe to do so, we could trace through it bit by bit and eventually answer that question.
It is correct to say that it is just science and math, the same way we can say that gravity is just science and math even if we have only recently begun to understand how it truly functions.
If you can distil the model's reasoning for a decision into a billion yes/no questions, each covering largely-independent areas, can you really say you understand what its overall reasoning was?
That is to say, we don't know why they give the outputs that they do.
If we did know how they worked, AI interpretability would not be an open and growing field.
To be clear I don't think that LLMs are sentient, but the appeal in studying them is similar to biology in that you get to dissect a highly complex system with comparatively crude tools.