If the neurologist were opining on politics, yes.Arrogance is the wrong word. I have accomplished things in my life through hard work and I know who I am. I do not think I am better than anyone else but I do know what I know. Others have not learned as much. The are no lesser people but less knowledgeable.
Would you call a neurologist that knows his trait arrogant, if he knows that he knows more than you do?
You are comparing a science to an art.