I sort of think it’s a multi-pronged thing.

I think one of Trump’s advisors floated it for the easy to grasp reasons -
Proximity to the trade lane that’s beginning to open up through the arctic as the polar ice melts, and access to Greenland’s rare earth minerals as a way to not be reliant on China for them.

I also suspect that should the Trump admin ever gain control of Greenland (I don’t believe they would), but they would turn it into a penal colony as they attempt to turn the U.S. into a white ethno-state.

There’s the ego factor. The rest of the world is telling the man-child Trump no, so he’s trying to see if he can get away with it. He’s a psychopath who likes to see if he can enforce his will on others. It’s not even about the actual gains of the action, but about overcoming the objections of others because he’s fragile and weak inside.

And finally - because if the U.S. looks like a credible threat to Europe, that means that Europe will have to invest in meeting that threat, even if the threat never materializes. Resources are finite and that harms Ukraine’s defense. No doubts from me that Trump is getting encouragement from his pal Putin to keep pushing for Greenland.

It is completely fucked, though. No ‘real’ U.S. citizen wants this, either.