A woman can only inherit a title from her father and only can use a title equal to that of her husband's title. Or maybe be given a title in her own right.
A woman can be a princess if her father is the King. She can be The Duchess of Florida if her husband is the Duke of Florida (for example).
A man and neither can a woman receive a title from their mother. The only time that has happened is when the mother is a heir to a throne or a monarch (Queen Regnant, the same as King-in-her-own-right).
When Princess Elizabeth (now, Queen Elizabeth II) married Philip Mountbatten. He was created His Royal Highness Philip Mountbatten, The Duke of Edinburgh by his wife's father. Because she was the heir to the throne and her father new that without the father of his daughter's children being a royal that would make his grandchildren not royal. So with the title his children were able to be styled as royal princes/princesses. Without that title Princess Elizabeth, Duchess of Edinburgh's children would've been commoners until their mother was put on the throne. Do you get the idea? The father is the person that needed to be royal.
Princess Alice, Countess of Athlone was married to the Earl of Athlone. The children were able to be styled as Lady or Lord. Not Prince and Princess. Their father was a peer not royal. Philip was created royal, so that Princess Elizabeth's children could bear a title...
History and Wikipedia