Some time ago it was very fashionable to fight for Tibet, but China was like a rock, so shortly thereafter people suddenly started yelling the same slogans but about Greenland and people felt a bit confused. Let's just say the modern day situation between Denmark and Greenland is different than China/Tibet. They have home rule, meaning they pretty much function as a independent country, and they get huge sums of money from Denmark to keep the country running and get it back on it's feed after all the abuse they suffered under Denmark. If they become fully independent they'd lose the money, so for now they choose to stay part of Denmark until they figure something better out. They vote on whether they want to become independent every so often, but so far it has always been a no. But worry not, it will happen some day.