I know nothing of the circumstances of this particular child (or Denmark in general) but I know of a few people born in various countries who are not citizens of that country because either the parent who was a national of that country couldn't be bothered filling in the paperwork, the parents thought they would be returning home sooner rather than later and therefore it wasn't necessary or the parents felt that they were of country x not the country of birth and therefore made sure that the child got the other nationality instead.

On the first point, I suspect it's part of the same legal tradition that includes the Code Napoléon, which did a lot to standardise the relationship between citizen and government, often in a different place to where the British would put it.

On the second, it's pretty clear - the parents are both Germans, and had made no efforts to secure anything other than German citizenship for the child. I have no idea how easy it is to claim Danish citizenship, but in a sense it doesn't matter anyway since it wasn't the parents' first choice of how to proceed.