When I say "America," I mean the executive branch, the one that signs treaties and moves ships, not the electorate. I don't think "the people" ever gave a shit about Greenland because they were too busy trying to put food on the table,but if we are to understand America as a super-organism that will go on for ages to come, then the idea of acquiring Greenland precedes and will transcend Trump's presidency. In the grand scheme of things, it actually does make sense.
As the Arctic waterways start slowly melting, America and every country surrounding that space is going to want to secure their dominance in the region. Owning Alaska and Greenland basically guarantees American supremacy over the Northwest Passage. Greenland also potentially has a metric fuck ton of rare earth metals that would reduce dependence on China almost completely. Owning that not only secures independence on substances necessary for military hardware (as I understand it) but it also ensure that you're enemies can't mine it for themselves.
There's also the matter of Russia arming their arctic north while Canada sort of sits there twiddling its thumbs doing nothing to ensure security in that region and if America is entering a multipolar world, they aren't exactly going to allow that to continue in there backyard.
With the exception of security from potential Russian aggression in the North, these weren't realities 70–150 years ago. These are emerging issues and saying "Trump wants natural resources" doesn't tell you anything.
Let me try again.
One day, with or without Trump, America will own Greenland.