The letter in question was not initially shared by MM's father.
Five of her closest friends brought it to the public's attention in an article in People magazine WAY before Mr. Markle said a thing.
The friends alluded to the entire alienation and estrangement being Mr. Markle's fault, and that MM's letter was a reaction to that. Mr. Markle had not uttered a word at that point.
Mr. Markle then shared the letter in his own defense, to prove that he was not entirely at fault for the rift since he had been misrepresented in by her friends in People. Mr. Markle did not care for being publicly misaligned, and he reacted.
It is up for debate whether a letter someone writes is the intellectual property of the writer or the property of the intended receiver. Most feel that it was Mr. Markle's letter to publicize or keep private by his own choice, once he received it in the mail. I am not a lawyer and I don't know the answer to that..
Please don't pounce; I'm just trying to add some info to the discussion and not taking sides. Rest assured that I am not a royal expert, but I DO think t is important to be informed before forming an opinion.
There are those that believe MM put her friends up to the People article. Otherwise, the idea of said friends even knowing about the existence of the letter would be without explanation. Without her explicit permission, to reveal the letter and its contents in an unapproved interview would have been unusual, unwelcome, and not advisable by the Royal Family's advisors, as is usually required. If the five friends spoke out of turn, a lawsuit would have occurred after the article was published in People, against the magazine and the 5 friends.
The letter was publicly discussed n the People article by MM's friends WAY, WAY before her father released its contents.