Your point rings true with most human reasoning most of the time. Still, at least some humans do have the capability to run that deductive engine, and it seems to be a key part (though not the only part) of scientific and mathematical reasoning. Even informal experimentation and iteration rest on deductive feedback loops.
I've never heard about the Wason selection task, looked it up, and could tell the right answer right away. But I can also tell you why: because I have some familiarity with formal logic and can, in your words, pattern-match the gotcha that "if x then y" is distinct from "if not x then not y".
In contrast to you, this doesn't make me believe that people are bad at logic or don't really think. It tells me that people are unfamiliar with "gotcha" formalities introduced by logicians that don't match the everyday use of language. If you added a simple additional to the problem, such as "Note that in this context, 'if' only means that...", most people would almost certainly answer it correctly.
Mind you, I'm not arguing that human thinking is necessarily more profound from what what LLMs could ever do. However, judging from the output, LLMs have a tenuous grasp on reality, so I don't think that reductionist arguments along the lines of "humans are just as dumb" are fair. There's a difference that we don't really know how to overcome.
Though note that as GP said, on the Wason selection task, people famously do much better when it's framed in a social context. That at least partially undermines your theory that its lack of familiarity with the terminology of formal logic.
It's as simple as that. In common use, "if x then y" frequently implies "if not x then not y". Pretending that it's some sort of a cognitive defect to interpret it this way is silly.