The author is right to say if an humble person does not reply to an arrogant person because he does not want any confrontation with him then his silence should not be considered that he agrees with him. Self-assertive people are always pushy to get their views and arguments accepted by everyone. They are so much aggressive that contradicting their views or rebuttal to their arguments may enrage them. So, in this situation sagacious and considerate people don't reply to them which they assume as their consent.
The bilateral argument is a good process to increase knowledge. Both of them are benefited by healthy arguments and discussion. When another person shares his knowledge and experience which we are not aware of, it benefits us. The best way to learn more knowledgable from people is that we should be a good listener. When someone is paid attention to what he says he is encouraged to keep on sharing his knowledge with a good listener.
The issue which the author has raised can be moulded in our way, keep on listening to what he says instead of debunking his views despite knowing that his views are not correct. However, we may expound him politely where he is wrong. We should not be aggressive to him because we know what his nature is. The best way to deal with such a person is either change the topic or move away from there.