Something to do with being the grandchildren of a reigning monarch, putting it simply. All of the Queens grandchildren born to a son (ie William, Harry, Eugenie, Beatrice, Louise & James) can be HRH Prince/Princess but Edward & Sophie didn't want to. The Queen decreed that all of Will's children would be princes/ses and I wouldn't be surprised if Harry's baby gets the same, after all he/she WILL be the grandchild of a reigning monarch if Charles takes over.
The rules seem to chop and change and there are several members of the family, such as the Queens cousins who are Princes but don't use the title for every days use.
Here's an official list of current/living British princes and princesses in age order, not all of whom use the title:
Philip 1921 Husband of
Queen Elizabeth II
Also a female-line Gt-gt-grandson of Queen Victoria Prince of Greece and Denmark from birth until renounced title 18 March 1947; Duke of Edinburgh – 1947; Prince of the United Kingdom (created by the sovereign) since 22 February 1957.
Elizabeth Alexandra Mary 1926 Daughter of George VI Held the title 'Princess Elizabeth of York' from birth, 'The Princess Elizabeth' from her father's accession in 1936, until her succession in 1952 as
Queen Elizabeth II.
Edward George Nicholas Paul Patrick 1935 1st son of George Edward Alexander Edmund
& Grandson of King George V Prince of the United Kingdom from birth; Duke of Kent since 25 August 1942.
Alexandra Helen Elizabeth Olga Christabel 1936 Granddaughter of George V Daughter of
Prince George, Duke of Kent.
Michael George Charles Franklin 1942 2nd son of George Edward Alexander Edmund
& Grandson of King George V Prince of the United Kingdom from birth.
Richard Alexander Walter George 1944 2nd son of Henry William Frederick Albert
& Grandson of King George V Prince of the United Kingdom from birth; Duke of Gloucester since 10 June 1974.
Charles Philip Arthur George 1948 1st son of Queen Elizabeth II Prince of the United Kingdom from birth; Duke of Cornwall and Duke of Rothesay – 1952; Prince of Wales since 26 July 1958.
Anne Elizabeth Alice Louise 1950 Daughter of Elizabeth II Held the title 'Princess Anne of Edinburgh' from birth, 'The Princess Anne' from her mother's accession, and styled 'The
Princess Royal' in 1987.
Andrew Albert Christian Edward 1960 2nd son of Queen Elizabeth II Prince of the United Kingdom from birth; Duke of York since 23 July 1986.
Edward Antony Richard Louis 1964 3rd son of Queen Elizabeth II Prince of the United Kingdom from birth; Earl of Wessex since 19 June 1999.
William Arthur Philip Louis 1982 1st son of Charles Philip Arthur George
& Grandson of Queen Elizabeth II Prince of the United Kingdom from birth; Duke of Cambridge since 29 April 2011.
Henry Charles Albert David 1984 2nd son of Charles Philip Arthur George
& Grandson of Queen Elizabeth II Prince of the United Kingdom from birth; Duke of Sussex since 19 May 2018.
Beatrice Elizabeth Mary 1988 Granddaughter of Elizabeth II Daughter of
Prince Andrew, Duke of York.
Eugenie Victoria Helena 1990 Granddaughter of Elizabeth II Daughter of Prince Andrew, Duke of York.
Louise Alice Elizabeth Mary 2003 Granddaughter of Elizabeth II Daughter of
Prince Edward, Earl of Wessex; styled as an earl's daughter per her parents' wishes and the will of the Queen.
James Alexander Philip Theo 2007 Son of Prince Edward & Grandson of Queen Elizabeth II Styled as an earl's son per his parents' wishes and the will of the Queen.
George Alexander Louis 2013 1st son of Prince William & Gt-grandson of Queen Elizabeth II Prince of the United Kingdom from birth.
Charlotte Elizabeth Diana 2015 Great-granddaughter of Elizabeth II Daughter of
Prince William, Duke of Cambridge, holds the title 'Princess Charlotte of Cambridge'.
Louis Arthur Charles 2018 2nd son of Prince William & Gt-grandson of Queen Elizabeth II Prince of the United Kingdom from birth.