Yup, arrogance is a symptom of incompetency. People are loudest about the things they are unsure about. We see it all the time in our line of work - beginners are the most arrogant. But it applies to doctors, lawyers, and psychotherapists too.
My dad's cardiologist is one of the best doctors I've ever encountered. His online ratings are all over the place and MOST of the low ranking patients were calling him "arrogant" and "terrible bedside manner".
The kid's probably more arrogant than the old man, too. But he's got to earn it.
But that is orthogonal to my point, a lot of doctors, lawyers, etc. are not any more arrogant than the average person; they just get labelled that way because people don't like being told they are wrong or getting bad news.