Subject matter expertise is, however, quite a difficult point. While I think most of us would agree that critical thinking is independent of subject matter expertise, it doesn't mean that I can blythely take my universally applicable critical thinking skills and confidently overrule the judgment of subject matter experts.
So if the dermatologist say the thing on Aunt Betty's arm is a harmless skin tag, and I, armed with Google and my critical thinking skills say its cancer, who should Aunt Betty believe? The doctor, or her idiot nephew Googling symptoms?
But here's the problem: sometimes you *can* be more right than someone with more expertise than you. I've actually been the idiot telling the doctor he was wrong, and ended up being right. The attending physician thought a family member was having a psychiatric episode, and I, a non-doctor, thought it was encephalitis. And in fact it was my critical thinking skills that allowed me to spot the errors she was making and challenge them. To her credit, when she couldn't answer my objections she brought in a neurologist who immediately confirmed my suspicions.
Logic really isn't the problem. In real life, sure, sometimes people affirm the consequent or something like that, but the big problem is evidence -- gathering it, evaluating it, and weighing it. Real life situations are full of red herrings and bad data and it's always necessary to pick some data to focus on and not others. The flip side of this is that it's always possible to obstinately challenge experts even when they're *right*. But they're not always right, or even justified.
So really the argument you need to have isn't about logic, it's about evidence is included and what is excluded, understanding that including and excluding is a necessary process.