Trump wants Greenland because he wants to be in the elite club of Presidents who expanded US territory. Only 4 Presisents are in that club: Jefferson (Louisiana Purchase), Polk (Mexican Session + Pacific NW treaty), Andrew Johnson (Alaska) and McKinley (Hawaii).

Trump knows that Denmark will let the US do any "strategic" thing in Greenland that he wants. But Trump wants to join the above club so he can be a "great President".