I think the main reason he refused Carolina was the fact that Cam Ward is signed long term, and seen as their franchise goalie.
Andersen wants to be the starter down the line, but he realize that he is not there yet. Surprisingly he has stated that he doesn't mind to spend time in the AHL, as long has he sees that there is a possibility to obtain the starting job in the NHL at some point. Obviously he and his agent didn't feel like that was possible in Carolina.
I also think that even though he had a great season in the SEL, he would prefer to stay there for at least one more season. I believe he had offers from Sweden before eventually signed with Frölunda, but he opted to stay in the danish league for another season. Which means that he has actually only seen one season of professional hockey (outside of Denmark) so far in his career.
Interpret it the way you like, I think it shows that he is not in a hurry. He'll get where he wants to been, when the time is right.
On a side note, staying in Europe next season means that he will be available for Team Denmarks Olympic qualifier in February. That means a lot for a country who has never produced any quality goalies before.