In the case in the article the author believed they were the expert, and believed their wife should accept their argument on that basis alone. That isn't authority; that's ego. They were wrong so they clearly weren't drawing on their expertise or they weren't as much of an expert as they thought, which often happens if you're talking about a topic that's only adjacent to what you're an expert in. This is the "appeal to authority" logical fallacy. It's easy to believe you're the authority in question.
...we’ve allowed AI to become the authority word, leaving the rest of us either nodding along or spending our days explaining why the confident answer may not survive contact with reality.
The AI aspect is irrelevant. Anyone could have pointed out the flaw in the author's original argument, and if it was reasoned well enough he'd have changed his mind. That's commendable. We should all be like that instead of dogmatically holding on to an idea in the face of a strong argument against it. The fact that argument came from some silicon and a fancy random word generator just shows how cool AI is these days. You still have to question what it's saying though. The point is that sometimes it'll be right. And sometimes it won't. Deciding which it is lies entirely with us humans.