I read that the Earl of Mountbatten discussed with King George VI about making Philip a Prince of the UK & that The King refused. I always wondered why was George VI so set against making Philip a British prince?? I mean he and Elizabeth (at the time) were of equal status... like her he was a prince from birth and an HRH.
This is commonly attributed to some combination of "the King didn't like Prince Philip" or "the (then) Queen didn't like Prince Philip," but that's not exactly accurate. The thing is that regardless of whatever George VI or his wife felt towards their son-in-law, the man wasn't exactly the ideal consort to a future British monarch.
For starters, the DoE and HM were not on the same level. HM was the daughter of the monarch and, at the time, the heir presumptive. The DoE, on the other hand, was the grandson of a deceased monarch and cousin to the then current monarch, making him more on the level of the Gloucesters or Kents.
Secondly, while the DoE's belonged to the Greek and Danish Royal Families he was of a questionable background given the time - in the post-war period even being foreign wasn't exactly desirable. The DoE's mother was ethnically very German - two of her grandparents were born in Germany, a third in Poland, and her father was born in Austria. He had four sisters who collectively married five German men, one who was a member of the SS and another who fought in the German army during the war. The DoE had gone to school in Germany for two years before moving to Gordonstoun. That said, the DoE was very British in his connections - his mother was born in Britain, as was his maternal grandmother (who had been the granddaughter of Queen Victoria), his maternal grandfather had held an important role in the British navy, and his uncle, Earl Mountbatten, was a very significant British statesman. He was a very British candidate for consort, he just wasn't necessarily British enough.
There is also the question of the DoE's British family, though. As decorated as Louis Mountbatten was, he certainly has proven to be a bit pushy when it comes to his royal nephew's family. The BRF tends to prefer that in-laws stay more in the background, but Louis Mountbatten wasn't exactly one to do so. He wanted his nephew, and his family, to be as important in this marriage, as the Princess' family, which wasn't exactly appealing to the Princess' father. Prior to the marriage, the DoE was not equal to his bride-to-be. At best he was a junior member of a foreign royal family who had essentially grown up in exile from his native country. If we take into account the fact that he renounced - regardless of whether or not he legally and formally did so is irrelevant - his titles then entering into his marriage, the DoE was little more than a British naval officer who had aristocratic and royal relations. I think, ultimately, George VI wanted to keep his son-in-law and his son-in-law's family in check a bit, and was able to do so by not creating the DoE a Prince of the United Kingdom.
There is also the fact that overall, the Princess Elizabeth was higher than her husband-to-be, and the King felt it important to keep her higher than him. When marrying someone equal to or higher than them women tend to lose their status and instead take on their husband's. This isn't necessarily true of royal women who marry men who are beneath them, or at least beneath them in the realm that they are royal. If George VI had made his son-in-law a Prince then his daughter would have become Princess Philip, much like how Kate is now Princess William even if she doesn't normally use that title. By making him just a Duke, albeit one with the style of HRH, the King ensured that his daughter's status wasn't diminished through her marriage. It's with this same kind of logic that the DoE isn't now King Consort - giving him a title equal to his wife's diminishes her status.