I think there are a few things going on.
Trump is very buoyant after the Venezuela stunt and wants to maintain that feeling. I think in particular he was very excited by watching the live action events of the Venezuelan kidnapping and he wants to see the sequel, like it’s a movie or something.
He is doing badly at home- affordability is becoming a big issue in the US and it’s affecting his popularity. So this is a distraction.
This also blows all the lingering Epstein coverage off air.
Trump does want to go down as a president who vastly increased the teritory of the US. He loves the thought of himself as a real estate mogul par excellence. He has employed some very aggressive property acquisition techniques in business and sees this as an extension of that.
He is both transactional and vengeful. So he sees this as striking back at people who refused him and made fun of him when he offered to buy Greenland during his first presidency. He does like lashing out in retaliation.
There is the question of trade routes as well as mineral rights and military presence. As the polar ice cap melts new shipping routes become possible and profitable that far north. Not only would control of those routes be lucrative, those routes would also mean increased shipping from countries like China and Russia going closer to the US than the US is used to and they are wary of that.
He’s made quips about the Monroe doctrine along the lines of “many people are now calling it the Donroe doctrine”. He really is taking an expanded view of how much influence the US should have over the whole of the Americas, from northern most to southern most tips. I think there are a variety of factors in this. Firstly, given his transactional nature he wants to reward the Latino male vote who swing towards him, and things like threatening Cuba, weighing in Venezuela are both macho and please the ex-pats from those countries in particular and territorial expansion is also macho. I do think there are grandiose notions of building a US hinterland/empire all throughout the continents. And there’s also lashing back at Canada for the way Canada handled tariffs.
Similar to the growing awareness of the possibility of trade routes opening up as polar ice melts, I think there is also some notion that parts of the US will become less habitable as climate change progresses and so more territory might be necessary. I know he presents as a climate change denier but I think it’s just actually more that he just wants to keep making money/gaining power to be well placed to ride out and profit from the changes, and a front of denialism is the best route to that. There’s definitely something of reich and lebensraum over this whole thing I think.
To be honest if I was Iceland I’d be pretty worried by all this too. they are!’t far off the coast of Greenland.
I think a subsidiary consideration is wanting to exploit this for leverage in the Ukrainian situation. He knows that European/NATO countries are aware that in order to safeguard the assistance the US giving Ukraine and by extension Europe, they need not to piss him off by standing up to him too much over this. So he is looking to extract what value he can by having them between a rock and hard place. Either way he wins, he either gets Greenland or him gets to back out of Ukraine. At the very least he gets to see European leaders squirm, especially given the US’s insistence for many decades on military interiperability between NATO members, so effectively many forces cannot effectively operate independently of US command and it would take a long and expensive spell of rearmament for the European countries to get out of that bind. This whole situation puts more pressure on the political situation in many European countries individually and on European co-operation in many levels. And there are a lot of vested interests, from Russia to tech giants to Trump himself who would like to see Europe weak divided and fractious.
Anyway, that was a bit of a wall of text. But you get the gist.