ok - lets repeat this AGAIN. Bearing in mind that George was born in July 2013
"On 30 November 1917 letters patent were issued declaring that henceforth only the children of the sovereign, sons of sons of the sovereign and the eldest son of the eldest son of the Prince of Wales would be entitles to the style of Royal Highness and the titular dignity of Prince of Princess."
so under this the first born child of William, if a female, would not be entitled to be princess. However, due processes were in place to equalise male and female children
"The Succession to the Crown Act (2013) amended the provisions of the Bill of Rights and the Act of Settlement to end the system of male primogeniture, under which a younger son can displace an elder daughter in the line of succession. The Act applies to those born after 28 October 2011. The Act also ended the provisions by which those who marry Roman Catholics are disqualified from the line of succession. The changes came into force in all sixteen Realms in March 2015".
ie they pre-dated George's birth. If the first child had been a girl, she would have been in direct line of succession but would not be entitled to be princess on birth - that title would be awarded to the first born son of the son of the sovereign. Hence the variation to the 1917 letter patent
"On December 31, 2012 Queen Elizabeth II made an amendment to the 1917 Letters Patent by issuing a Letters Patent which gave the title and style His/Her Royal Highness and Prince/Princess of the United Kingdom to all the children of the son of the son of the sovereign".
would you want to go backwards on female equality?
This was done before any child of William was born, to avoid all the female equality issues which particularly effected Princess Anne, for example.