Why was Diana princess but not Kate Middleton?

Answer 1

Because Charles was first in line to throne and therefore Prince of Wales when he married Diana. She then became The Princess of Wales upon marriage. William is second in line to the throne and not The Prince of Wales (yet). He was created the Duke of Cambridge upon his wedding day and so Kate became The Duchess of Cambridge. She is however also "Princess William" just as a married woman can be Mrs John Smith. When Charles is King, William will become Prince of Wales and Kate Princess of Wales.

Answer 2

This is because Kate was a commoner.

While it had been tooted before Diana got married that she was a commoner she actually was the daughter of a Earl and herself was styled "Lady Diana Frances Spencer" before the wedding. She could also claim royal descent as she was the direct descendant of Charles II from several of his illegitimate children.

Kate however actually was a commoner even though there is specualtion that she is actually a descentant of Henry VIII (via the daughter he had with Anne Boleyn's sister Mary.) Therefore she herself is not eligible to be styled Princess Catherine and why she is refered to simply as Duchess of Cambridge

Answer 3

As Prince Charles is the Prince of Wales, Princess Diana became a princess automatically after her marriage.