Rare earths aren't rare
Trump wants Greenland, but it's not because of its rare earth reserves.
If there's one thing I've learned about Trump, it's that you should take him literally. When Trump says he wants something, he means it. That doesn't mean he'll get it, or that he won't eventually chicken out; but if he says he wants it, then he definitely wants it.
Enter Greenland. Over the weekend, Denmark and several European nations dropped a few dozen troops in Greenland under Operation Arctic Endurance. The US was invited, but instead of joining, Trump fired off a long tweet on his Truth Social platform threatening all involved with 10% tariffs on 1 February, increasing to 25% on 1 June, "payable until such time as a Deal is reached for the Complete and Total purchase of Greenland".
Why is Trump so keen on Greenland, which is anything but green? The media likes to report that its minerals are what's important; oil and gas, but specifically rare earths, given China's recent flex in that space. That's despite Trump himself once stating:
"We need Greenland for national security, not for minerals... There's no such thing as rare earth."
On the latter, he's factually correct:

Note that some of these reserves, especially in Greenland, are unproven, unextracted, encased in difficult geology, co-located with uranium that Denmark has banned it from interacting with, have zero infrastructure, and are in some of the world's most expensive mining jurisdictions.
If Trump was really concerned about supply then some kind of strategic stockpile would be considerably easier and cheaper than acquiring an entire country. Which leaves Trump's own words as the reason he wants Greenland:
"The United States has been trying to do this transaction for over 150 years. Many Presidents have tried, and for good reason, but Denmark has always refused."
Strategic access to thawing Arctic channels, the "Dome", critical minerals; all could be secured, achieved, or acquired under Danish ownership.
Trump wants Greenland because he's obsessed with the late 1800s, a period during which President Johnson purchased Alaska (1867) and President McKinley passed a bunch of tariffs (1890). He even invoked "manifest destiny" in his inaugural address, stating that the US would again become a nation that "expands our territory".
Take what Trump says literally and seriously. Greenland is just a big real estate deal for a guy who has spent his life in real estate, is clearly obsessed about his legacy, and fancies himself as a nation builder.
Nothing more, nothing less.