Yes, they do not want to be ruled by anyone.

And that includes China. Your argument makes no sense. There is no talk in Denmark to stop to support Greenland. In contrast, they increase spending. That includes especially increased spending to protect it.

Interestingly, the US has massively reduced its military presence on Greenland and is not investing in polar defence capabilities. The security argument is not credible.

In case of the Virgin Islands, you are referring to an event in the middle of the First World War - a completely different time. The Virgin Islands were at the time a colony. Greenland today is not a colony of Denmark. The rights of the people in Greenland are very different from it had been in 1917. Not everybody has still an world-view from the 19th or 20th century.

You comparing Greenland with much poorer countries. The median income in Greenland is 21x higher than in South Africa and 33x higher than in the Salomons.