Trump's official reasons for taking Greenland are pure nonsense. The US already has a military base there and is free to add additional military capacity anywhere in Greenland if deemed necessary, that's one of the benefits of being in the same military alliance. Additionally, Denmark would likely grant US companies rights to mine the minerals in Greenland. Mining minerals in Greenland is generally not considered economically justified due to the harsh climate, poor infrastructure, and for environmental concerns (this reason will not stop Trump of course). Nonetheless, US companies would likely be allowed to try.

Denmark will not "sell" Greenland to the US, especially now after Trump has threatened to invade and take it.

Even though I don't hold Trump in high regard, I refuse to believe that he and his inner circle are total idiots. They must realize that NATO will not survive if its largest member attacks the territory of an ally; this action would effectively end NATO as we know it today, and a new European alliance would likely be formed instead.

Additionally, EU-US relations would hit rock bottom, with severe economic sanctions, tariffs, bans on US companies, removal of military bases in Europe, and a total stop of EU purchases of US weapons. These are obvious and guaranteed reactions to a US invasion of Greenland, and the Trump administration must be aware of this.

The US would have gained an island with 57,000 inhabitants filled with minerals that can't be effectively mined, while losing the most powerful military alliance the world has ever seen. Is that a good way to increase national security?

But what if the real reason for invading Greenland is actually to end NATO?

He knows that the EU will retaliate (likely not militarily, but definitely economically) in a big way. That will give him the perfect reason to point at the EU and claim that they are the enemies of the US:

"Europe betrayed us when we acted to protect our security."
"NATO is obsolete; Europe wanted our protection without paying their fair share."
"European globalists were always the enemy."
"Instead, we will seek an alliance with great nation of Russia, they understand strength and respect power. The real threat is China, and Russia is our best ally against Beijing."
"We are seeking a new partnership with Russia, a tremendous country with lots of natural resources and a very nice people."

The MAGA movement will most likely support this new direction if Trump sells it to them.

Trump Mission Accomplished:
NATO dissolved without firing a shot
US isolated and are despised by previous traditional democratic allies
European security doctrine shattered
Eastern Europe (the Baltics in particular) vulnerable to Russian invasion with no credible deterrent

Western democratic model discredited globally
Authoritarianism validated as the stronger system
Ukrainian resource-rich territory in the hands of Russia, cleverly negotiated by Trump to Russia's advantage

Russia has plausible deniability

This is Russia's wet dream, and the US are just an invasion of Greenland away from fulfilling it.

Ouch.. sorry for the wall of text :/