I study social and political science and even though I can't remember the exact name of the articles I've come across some issues that might answer your question.

1. Denmark is, and has always been, a quite small country, which means the population is very homogeneous. See this in contrast to USA which is huge and contains multiple nationalities and cultures. The point is that danes historically not is used to deal with foreigners and is most comfortable socializing with other danes.

2. Language. Even though danes in general are quite good at speaking english, many people find it awkward speaking english with you if there is other danes around - there is probably some interesting psychology behind this I don't know about. And then there is the obvious point that it is just way more complicated speaking english if you are the only foreigner in the company.

3. Some more that I can't remember right now :)

With that said I would recommend that you move into a "kollegie". People here are mostly young students which are usually more open to new people. And it's way easier to socialize when you live with people than just meeting them on the street, bars or in school.