To understand what is going on, you need a bit of Geography, a bit of Law of the Sea, a bit of History and a pinch of salt.
History lesson: The story of Arctic exploration dates back two millenia - the fact that their ships were cracking, that they got stuck in ice half the time and the a good part of their crew died of cold never stopped explorers for setting out to discover the great North. Inuit populations arrived first, exactly when isn't clear. They started to see visitors - and at the same time discover they weren't alone in the world - when Viking explorers arrived. The Vikings were among the first to visit and settle in Iceland and Greenland, despite the harsh life conditions you found there.They were followed by more explorers from Europe - Dutch, British, French, you name it. They explored for all reasons: pure science, money, or expanding their home country's land claims. Slowly, all those various claims were settled down. Hans Island is one of the very few that are still going on.
Geography lesson: Hans Island is located in the middle of the Nares Strait, which separates Greenland and Canada's Hans Island. There are two other Islands in the same channel, but they are just a bit closer the Greenland. None of all these islands is inhabited. There is no economic life possible - no animals to hunt, no vegetation growing, nothing. What's interesting is what's around them: the sea, with fish and possible oil in the ground.
Here's where Law of the Sea comes in. Land dominates the Sea, and if you have the land territory, you can get maritime zones around them. For rocks that have no economic life, you cannot obtain an exclusive economic zone or a continental shelf, but you still get the 12 nautical miles territorial sea. Considering how narrow the Nares Strait is (20 nautical miles at its widest), that's big enough - you wouldn't get an EEZ anyway.
Finally, for a pinch of salt: Canada and Denmark have a very strange way of disputing this island. Icebreaker patrols are set, and once in a while, Danish or Canadian soldiers set foot on the island to remind the other of their claim - prompting ironic headlines of "invasion from the other country's newspaper. Regularly, a high ranking official from Denmark or Canada is shipped to the island. They will bury a bottle of national alcohol, plant a national flag on top and leave. A few years later, the other State will ship a high ranking official who will dig up the other bottle, take out the flag and replace both by a bottle and flag of their own, and leave. Remember: if you're from Denmark or Canada, this is your taxpayer's money at work. I suggest paying your taxes in beer next time, it will go faster.

Some have decided to take this dispute even further. Two spoof organizations, the Hans Island Liberation Front and Radio Free Hans Island have decided to mock Canada and Denmark all the way - but how can you ridicule something that's already a caricature of itself?

Sadly, all this is happening while there are much more important threats facing the Arctic. Glaciers are melting right next to Hans Island, testimony to how serious a threat climate change is. It's time to face the real challenges of the Arctic and stop dealing with world politics like a preschool playground.