The way Trump views everything and everyone around him are as winner/loser, master/slave, dom/sub type relationships. I think he genuinely believes the USA has fallen into the loser nation category hence "make america great again". Apparently his first term didnt fix that. Europe, especially the smaller nations in it, fall further still into the loser category because they rely on America for defense. It's been a long term gripe of Republicans that the USA contributes the most to NATO while Europe with a few exceptions doesn't even contribute 5% of their budget.

Taking Greenland means a few things: securing the future of the USA even when it won't have the fighting power it has now, pressuring the Euros to increase military spending and reduce social spending, and making Trump look important which he likes.