Why are aristocratic titles (duke, earl, etc.) still relevant to the British in the 21st century?

As an American, I am curious as to how an antiquated aristocratic system still holds such sway over the British people. I was reminded of this by reading a news article about Andrew, the Duke of York and his role as a British trade representative. The article referred to him as "his royal highness". How does someone, in this day and age, still seriously refer to another person as a "royal highness" without considering the absurdity of it it all? Of course, the ultimate question related to aristocracy is why is a monarchy still valid? Is there something in the psyche of the average Brit that needs to be subservient to someone of a perceived higher social status?