There is much more to the story than his drinking. According to “Rytterkongen” - the authorized biography on Christian X written by professor Knud J. V. Jespersen - Frederik’s proposal was somewhat impulsive, and the Crown Prince confided to a friend that he had second thoughts already the next day. A few weeks after the betrothal he went to Athens to meet Olga again and to spend time with her family. Jespersen writes (translated from Danish):

"During their daily interactions, the two young people soon realised that they were not at all suited to each other. What should have been confidential talk between new lovers turned into formal conversation instead, and apart from the occasional kiss on the cheek, there was no physical contact. When the Crown Prince asked hopefully whether Olga was not looking forward to coming to Denmark, she simply replied sullenly and dismissively that she was supposed to. The whole thing gradually developed so sadly that the Crown Prince made it a habit in the evenings, after saying goodnight to his in-laws, to wander over to King Constantine's palace, where he sought - and found - comfort and support from the King's two eldest daughters, Helene, married to the Romanian Crown Prince Carol, and Irene, who was unmarried and a year younger than Princess Olga. The two lively young girls took loving and understanding care of the unhappy young Danish Crown Prince. And with Princess Irene in particular, he seems to have developed such a warm and intimate relationship that it could well resemble mutual infatuation, which of course further complicated his relationship with Princess Olga.
The end of it all was indeed a break-up. Just before the end of the visit, which was supposed to have confirmed the relationship between the two newly engaged, Crown Prince Frederik finally summoned up all his courage and openly told his parents-in-law that he no longer cared for their daughter and that it was all a misunderstanding. The father-in-law was furious and scolded the young man, while the mother-in-law almost dismissed it, thinking that things would be fine again and that they would just have to wait and see."