Why didn't Denmark sell Greenland? Some comments
Aside from the usual nationalist feelings about land, the Greenland population is ~25% genetically Scandinavian, presumably mostly Danish. This number is from genomic studies, the sociological counts differ somewhat because they include the mixed persons in the Inuit group ('one drop rule'). Generally, people don't sell land their own people live on. Russia sold Alaska, but few Russians were living in Alaska (Wiki says 700). The population count of Greenland was about 21,000 in 1946, so this would have meant selling the land of multiple thousand Danes and mixed Danes. At least assuming the admixture was similar back then.
Greenland (and Iceland which was lost during WW2) was the stage for one of the most glorious times in Danish history, namely the vikings' discovery of America -- even if this was done by a Norwegian and his son, people didn't distinguish so much between Scandinavians back then, and Denmark used to own Norway. On a side note: I don't know why English doesn't use his real Danish name which is Leif den Lykkelige (Leif the Blissful) and apparently the Norwegians call him Leif den Hepne (the lucky).
Regarding money, Greenland is a large deficit for Denmark. I found a number for 2014 of 3.6 milliarder kroner per year (530 million USD). The Danish state budget was about 162 billion USD in 2016, so this deficit to Greenland is about 0.32% of the state budget. In comparison, foreign aid was 2.18 billion USD and the EU net deficit is about 867 million USD per year (2015 data). Considering that there only are ~50,000 people on Greenland, this means that per capita, Denmark is contributing about 10k USD per person per year. In comparison, the average GDP per capita of the world (PPP) is about 15k USD per year and about 80 countries have lower GDP per capita than Denmark spends on Greenland. And Greenland still has a deficit.
There is not just the direct contribution, but also the number of Greenlanders moving to Denmark. Greenland's total fertility rate has generally been above 2 in recent history, but the population declined due to migration to Denmark. One government report mentions about 15,000 Greenlanders living in Denmark. Greenlanders are Danish citizens, so they do not appear in any official statistics I have been able to find/access, so I could not find any good income, crime, education etc. statistics for them. However, the government reports about them are generally negative in tone, so they are surely lower status than Danes and hence a net drain on resources. (The Danes are very close to 0 on the net benefit scale, so any lower group must be a deficit.)
The stereotype in Denmark about Greenlanders is that they are homeless drunks. One can often see some of them hanging out near shelters or drinking outside when the weather is halfway decent (drinking in public is legal in Denmark). On the personal side, I went to efterskole with 3 of them and all 3 of them were expelled for drug use/alcohol. In comparison, perhaps 5 Danes were also expelled that year. This is out of a total of about 100 persons, so the rate among Danes is something like 5% and 100% among Greenlanders. Assuming equal rates of expulsion of 5%, this gives a p value of .053 or 0.000125.