Arrogance is an interesting topic.
Let's imagine we have two people who are having a conversation. One of them is an professor in quantum mechanics and the other person is an enthusiast who has read a few popular science articles online.
The professor always gives his honest opinion, but in an extremely blunt manner, not holding anything back and not making any attempts to phrase it politely. That is, the professor does not merely tell the enthusiast that they are wrong, but also provides his honest assessment that the enthusiast does possess even a basic understanding of the core concepts of quantum mechanics.
The enthusiast is polite throughout, even when subject to this criticism. They respond to the professors objections about their viewpoints, to the best of their ability throughout, trying their best to engage directly with the professors arguments. At the same time, the enthusiast is convinced that he is correct - equally convinced as the professor in fact - but he does not vocalise this in the same way as the professor.
Who is the most arrogant in these circumstances? Is this even a useful question to ask - or should we be dividing arrogance into two components - over-confidence and dismissive behaviour?
Let's imagine the same conversation, but imagine that the enthusiast does not know that the professor is a professor and neither do the bystanders. The bystanders don't have a knowledge of quantum physics - they can't tell who is the professor and who is the enthusiast since both appear to be able to talk fluently about the topics. All they can see is that one person is incredibly blunt and dismissive, while the other person is perfectly polite and engages with all the arguments raised. Who would the bystanders see as most arrogant?