I think it corresponds to the number of non-native speakers. English speakers are used to hearing people from every corner of the globe speak our language, so we are pretty unfazed by an accent. Danes - like, I think, most speakers of languages that remain largely isolated to their land of origin, have no such exposure - and thus tolerance - to accented speech.
In my experience, most professional immigrants to Denmark have more trouble learning Danish than they would if they'd moved to Sweden or Norway instead.
Before I moved to Denmark, an hour with a Swede plus reading the back of Lonely Planet taught me enough Swedish reading and pronunciation to order food in the airport in Swedish. Danish takes weeks or months of exposure to get an ear for the language, plus more weeks/months of practise to be understood.
It's certainly possible; I know adults from all over Europe whose can speak Danish from reasonably to very well. It does take more effort and more motivation than elsewhere.
(I wrote professional, since this is based on a typical situation of a couple of hours of Danish class a week, plus homework. I can't compare children, other workers, refugees etc, as their situation is so different.)
That's interesting to hear. I must admit I am at least a little bit attracted to the challenge of learning a language that's known for being difficult, though of course the vast majority of what attracts me towards Denmark (over other Nordic and European nations) is lifestyle and political factors.
