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.