The New York Times interviewed Trump on why he wants to own Greenland and why security agreements and cooperation are not good enough:
The president’s insistence that Greenland must become part of the United States was a prime example of his worldview. It was not enough to exercise the U.S. right, under a 1951 treaty, to reopen long-closed military bases on the huge landmass, which is a strategically important crossroads for U.S., European, Chinese and Russian naval operations. The president’s insistence that Greenland must become part of the United States was a prime example of his worldview.
“Ownership is very important,” Mr. Trump said as he discussed, with a real estate mogul’s eye, the landmass of Greenland — three times the size of Texas but with a population of less than 60,000. He seemed to dismiss the value of having Greenland under the control of a close NATO ally. When asked why he needed to possess the territory, he said: “Because that’s what I feel is psychologically needed for success. I think that ownership gives you a thing that you can’t do, whether you’re talking about a lease or a treaty. Ownership gives you things and elements that you can’t get from just signing a document.”
In other words, it's not about national security concerns or not having access to rare earth minerals - it's all about feeling good about having a piece of paper that says he owns it.