Prince Harry's son, Archie Harrison Mountbatten-Windsor, is not a prince, whereas Prince Andrew's daughters, Princess Beatrice and Princess Eugenie, hold the title of princesses. This distinction arises from the difference in their royal lineage and the rules governing the allocation of royal titles within the British monarchy.
To understand this disparity, it is important to delve into the intricacies of the British royal succession and the historical protocols surrounding the conferral of titles. The system of royal titles and styles is rooted in centuries-old traditions and has undergone various modifications over time.
Prince Harry, as the second son of Prince Charles, falls into the category of a grandchild of the reigning monarch. Traditionally, only the grandchildren of the monarch through the direct male line (sons and their male descendants) automatically receive princely titles. In 1917, King George V issued a Letters Patent restricting the use of royal titles, which stipulated that only the children and male-line grandchildren of the sovereign would hold the title of prince or princess, with the exception of the eldest son of the eldest son of the Prince of Wales (currently Prince George, the son of Prince William).
Since Prince Harry is the second son of the Prince of Wales and not the eldest son, his children are not entitled to the princely title by birthright alone. However, Queen Elizabeth II intervened before Archie's birth and decided that Prince Harry's children would not automatically receive royal titles. As a result, Archie was given the courtesy title of "Master," rather than "Prince."
On the other hand, Prince Andrew's daughters, Princess Beatrice and Princess Eugenie, were born to a prince. Prince Andrew, Duke of York, is the second son of Queen Elizabeth II, making Beatrice and Eugenie her granddaughters. According to the aforementioned Letters Patent of 1917, they fall within the category of male-line grandchildren and thus receive the title of princess by right.
It is worth noting that the Queen has the power to bestow royal titles upon her family members, and she did so in the cases of her other grandchildren. For example, Prince William's children, Prince George, Princess Charlotte, and Prince Louis, were all born with the princely title due to the Queen's Letters Patent in 2012, which extended the courtesy title to all of Prince Charles's grandchildren.
The decision to exclude Archie from the princely title can be seen as part of a broader effort by Prince Harry and Meghan Markle to seek a more private life outside the constraints of the royal institution. They have expressed a desire for their children to have a more ordinary upbringing, free from the intense scrutiny and expectations that come with being directly in line to the throne.
It is important to understand that royal titles are not solely determined by birthright but are subject to the Queen's discretion and the historical precedents set within the British monarchy. The circumstances surrounding Prince Harry's son not being a prince while Prince Andrew's daughters are princesses highlight the complexities and nuances of the royal lineage and the protocols surrounding the bestowal of royal titles.