Undoubtedly this has been addressed, but in checking all topics under the Greek Royal Family I haven't yet found it.
From what I've read, Prince Christopher ("Christo") of Greece and Denmark courted and was briefly engaged to Princess Alexandra, the daughter of Princess Louise, Duchess of Fife, in 1910. But when Louise and her husband learned of the engagement, they promptly terminated it.
My question: Why did Alexandra's parents not approve of the engagement? Prince Christopher, to my knowledge, was not an objectiable young man. And as we know, engagements between royal cousins had happened before, and would happen again.