The engagement that got broken off.
Yes, for reasons that are known : Olga would have realized she was not in love with Prince Frederik and preferred instead to break a marriage of convenience. The future Frederik IX, cons, had great difficulty accepting the break and would not hear about marriage for years until he met Ingrid.
I read that was Fredrik who insisted on breaking the engagement as he realized that he didn't love Olga.
I'm pretty sure it's Olga, who told her parents that she did not love her Danish cousin and she preferred to break her engagement. Upon hearing the news, Princess Marina would have approved the decision of her sister, saying : " but seeing as she does not like him."
A recent article in the Royal Digest Quaterly by Trond Noren Isaksen is about broken engagement of Fredrik and Olga.
After reading the article I came to conclusion that both Fredrik and Olga were not delighted with the whole thing but it was F. who did the 1st step to break the engagement.
In February 1922 they met and F. was so taken with Olga that proposed her almost on the spot. Later he told to one of his confidantes that he had been carried away when he met Olga,but regretted his proposal already the next day.
Later they met again and Olga was very cool with him. Fredrik realised they had no future and said so to her parents, and then to his own parents. Both parties were horrified but tried to settle the matter and the young people met again in Paris half a year after the engagement. Olga said in her diary: "I said I was willing to try again but he said he had no more love for me".