. Danes are the second best (next to Belgium) in English among the nations whose mother tongue is not English. I doubt you can communicate well with them in English either.
Who told that you have to learn Danish? You have to learn Danish if you want to work and be a part of Danish society. I don’t know if it is your case.
English is not the official language of Denmark, and it is Danish. Official correspondences will be in Danish. Your children will go to Danish institutions.
If you want to live in Denmark permanently, you need knowledge in Danish to obtain a permanent residence permit.
Many Danes know French and German. Denmark is very international-minded country.
Danes are living in their own country. You are the one who is coming from another country. It is your obligation to learn Danish. Why should Danes speak English when they are home? They do when they travel abroad.
I learned Danish. My wife has learned Danish so good that she is now a teacher in the Danish language.
You are living in Denmark. It is you also your moral obligation to respect their language and culture.