I think your professor probably should have a talk with your class and explain the cultural differences between Denmark and the U.S. - is he even aware of some of the students having a problem with the way he speaks?
Hopefully he'll can modify the way he speaks, while his American students on the other hand can learn about a different way of communicating, and thereby they can meet each other half-way. Or at least have enough understanding so that no-one gets hurt or offended or your professor feels like he has to watch his every sentence.
That said...yeah, I'm a Dane and I once had an American friend in tears while I was just being friendly. Luckily we could talk about it because I was absolutely mortified that I had made her cry - a Danish friend would have laughed.
After living abroad for some years, I've learned to modify the way I speak according to whom I'm speaking with. I don't speak the same way to say my American, Swiss or Greek friends that I do to my Danish, Dutch, Norwegian, British or Australian friends because of the cultural differences.
I also try not to get frustrated when I cannot get a straight answer because being blunt is considered rude. The Greeks are particularly good at that, and I don't have the cultural background or experience to know that the answer is without them telling me directly, so we both end up frustrated with each other. Them at me for not getting what they are trying to tell me, and me at them for not directly telling me what it is they want because I honestly can't figure it out.
Your question btw. reminds me of my university days where on a field trip someone said to our professor "What the hell, Simon, didn't you make any coffee yet?" - some of our foreign students almost had a heart attack. ;)