The answer may be simple: that the Queen considered the photos Ms Leibovitz took of her in 2007 to be among the best of the lot.
Perhaps another factor ought to be included: that the Queen enjoyed Annie's company last time, and was happy to invite her back to the house (Buckingham Palace, that is).
It might be a stretch to say they are friends. Yet they understand each other. It is important to recall that the BBC commissioned a fly-on-the-wall documentary nearly a decade ago which, among other stabs at sensationalism, asserted that the Queen had been furious with Annie. Intentionally duplicitous editing, and the outright lie that Annie's stage directions caused the Queen to storm out, earned a stern rebuke from Her Majesty herself.
A few lazy articles about the 90th birthday photos revived the supposed 2007 tiff, despite glaring evidence that the feud was fabricated. What the gracious and extraordinary invitation to Ms Leibovitz for her 90th showed - besides the Queen's exquisite taste in photography - is that her staunch support in 2007 was no fluke.
They don't appear to have much in common. Annie is American, lesbian, Jewish. Despite an astounding career, not long ago she found herself in financial trouble. A substantial share of her photographs feature her family, which is really, really Jewish. New York, Florida; you don't get more Jewish than that.
The Queen's relationship with Ms Leibowitz underscores that she does not have a Jewish problem. The shrill, silly and mean-spirited spin on a moment of childhood Nazi play-acting merits mention only to be dismissed. Views expressed by her older relatives are troubling, but they have not inclined the Queen towards antisemitism - she has her own mind.
To the extent that the Queen can have friends, or even friendly relations with those outside of family, Annie Leibowitz isn't the first Jew with whom she has enjoyed a cosy relationship. Although he was primarily a close friend of her husband, the Queen had a not-exclusively-business-like relationship with the photographer Sterling Henry Nahum (known as Baron), who died in 1957. She appears cheerful and at ease in many of the photos Baron shot of her.
I would speculate that the Queen's level-headedness and general good sense in dealing with Jews as individuals and "things Jewish", since her coronation in 1953, also derives from taking her role as head of the Church of England more seriously than is often assumed.
One of my former students was vicar of a large parish which experienced serious social rifts and outbreaks of violence. While reticent in speaking of his private relationship with the Queen, he said that she made a point of meeting him in person and was truly interested in the goings-on in his
parish. She even asked, sincerely, what she might do to help.
I have no idea if the Queen meets regularly with non-Anglican clergy. But this indicates that she cares - which is unlike the way she is portrayed in the movie The Queen, which focuses on the monarch's response to the death of Princess Diana, the episode of her reign that casts her in the most disparaging light.
The Queen is a good film and Helen Mirren in the title role is fabulous. What I believe the filmmakers got wrong is making the Queen and Prince Philip humourless and snobby. They are neither. The royals do not live like "the people", but they do not think they are inherently above others.
Although my own experience with the Duke of Edinburgh is based on a single conversation of some 45 minutes, it focused on Jewish issues and his relationship with Baron. I would guess that his wife is as free of anti-Jewish prejudice as he is, and that, like her husband, she makes a point of paying little regard to the religious or social origins of those she encounters.
There are a few cranky Jews who believe that the Queen should be criticised for never having visited Israel. Considering the tempestuous history of the British mandate and its demise, and unresolved tensions in which politics and religion are inextricably intertwined, visiting Israel would be a minefield for the royals.
The Queen tries as hard as possible not to express her private opinions. How could this be avoided were she to go to Israel, where every word, every gesture, where one steps and where not, and with whom one speaks, is scrutinised and contested like on no other patch on earth?
There never has been a poll, but I would guess that the vast majority of Jews like the Queen, and many have a deep affection for her. Even some of the fierce republicans I know are careful to qualify that they hold nothing against the Queen, personally.
It may be that Jewry worldwide has stronger feelings for the Queen than do the Jews of Britain. Growing up in Rochester, New York, my family regularly watched the silent films my father bought, second-hand, from the Eastman Kodak Camera Club. One we viewed frequently was The Coronation of Queen Elizabeth II. We never thought of it as odd.
It may be significant that the Queen was thrust into her role much earlier than anticipated - in some ways like a young person obliged to take over the family business. She was in the same trap as a referee in professional sport - expected to be perfect at the beginning and improve over time.
She rarely is off the mark.
