To see that better, consider what I call "simplified Chinese room". It's a variation on a traditional Chinese room, where inside the room, there is only a pattern recognizer, which basically will match the input to arbitrarily many inputs (but not all possible) it learned before and chooses the output for the best match.
Now imagine I want to train this "simplified Chinese room" on solving satisfiability problem. Because in that problem, an arbitrarily small change in the input (introducing a contradictory clause) can completely change the output. It is therefore impossible, I believe, to learn the concept of satisfiability by just using pattern recognition (storing and comparing, according to some metric, previously seen inputs and corresponding correct outputs). Instead, you need to build a mental model which is internally self-consistent with these example pairs.