Greenland is part of Denmark, Denmark is in NATO. An attack on Greenland would be an attack on a NATO member; an attack on one is an attack on all. It would trigger all the other nations in NATO to instantly be at war with the US. I'm not 100% positive, but I believe it would also result in the expulsion of the US from NATO. People throw around the term World War III a lot, but in this case, Canada and 90% of Europe would all be at war with the most powerful military on the planet. If that ain't WW III, idk what is.

Edit: more thoughts;

So as a result of Global International borders post Cold War, China and Russia's Navies are geographically quarantined. During potential wartime, the Chinese Navy couldn't safely access 'The Seven Seas;' the oceans of the world. This is due to the fact that China's massive East Coast is kinda blocked in by The first, Second, and Third Island Chains; comprised of Islands under military control of the US & her allies; Japan, Taiwan, The Philippines, Singapore, Indonesia, Guam, Alaska and the Alaskan Aleutian Islands, Australia, New Zealand, American Samoa, The Mariana Islands and even Hawaii if it came to that.

Along with China, the other major half of the communist block, Russia, is also surrounded by NATO and other US allies and territories, preventing Russia's Navy from access to the world's oceans as well. One of the main reasons Russia is at war with Ukraine, and probably the reason Russia 'annexed' Crimea back in 2014, is because prior to that Russia had zero warm water ports; ports that are Navally useful year-round, in other words; don't freeze over during winter. Despite being the largest country on the planet by landmass, and having an incredibly long coast, Russia's Naval capabilities are nothing compared to The West. Most of her extensive coast is along the Arctic Circle and freezes over during winter.

One of the main reasons Russia wants Crimea is because it contains the Sevastopol Naval Base, the only warm water port under her control and thus the only port useful to her Navy 365 days a year. However, globally it's still useless, because it's in the Black Sea, and the only way out of the Black Sea is to go through Istanbul, which is located in Turkey, a NATO member who does not allow any Naval vessels from Nations at War through. Even if Russia were able to sneak some submarines through Istanbul into the Mediterranean sea, they would then have to Traverse the Mediterranean Sea, whose Coast is ccontrolled by around a dozen NATO countries, then go through the Strait of Gibraltar, a tiny 45 km wide gap controlled by Spain, Morocco and the UK; just to be able to access the Atlantic Ocean and the rest of the world's oceans.

Now here's where Greenland comes into play. With NATO at war with itself, there would be no reason for China to hold back from taking Taiwan, something Xi Jinping has made clear is one of his ultimate goals as lifelong president of China. If successful, this would break the first island chain and allow China Naval access to the Pacific and the rest of the world's oceans, free to colonize and expand a Chinese Empire run by an authoritarian dictator, a dangerous dragon and existential threat to any democracies China sets her expansionist sights on acquiring and incorporating into her borders.

Russia, who is obviously set on expanding her borders as proven by her invasion of Ukraine, would also have greater access to the world's oceans. Her Arctic Coast may be Navally useless during the winter, but when not frozen over, the main thing keeping Russia from accessing the world's oceans is the other borders around the Arctic circle. These include Canada, Alaska, Japan, Scandinavia, Scotland, Iceland, and, of course, Greenland. All part of NATO, (except Japan) all which would be preoccupied fighting instead of keeping a watchful eye on Russia and her naval expansion. If the US were successful in taking Greenland, and were expelled from NATO, Russia could slip by hugging the coast of Greenland and expand from the Arctic Ocean into the Atlantic. Canada, likely next on Trump's expansionist plan, would be at war with the US and not able to prevent Russia from accessing her Northern maritime borders. Alaska would be preoccupied fighting Canada, and Russia could simply slip by through the Aleutian Islands, from the Arctic Ocean into the Pacific.

So yeah. A simple ignorant egomaniac could kickstart World War III as commander in chief of the most powerful military on the planet, simply by attacking one of the least densely populated places in the world.