in practice a good majority of people support it and basically see it as "community service", with it being more relaxed than US service and most people doing jack shit for several months (it's also not really mandatory since you can get out with conscientious objection and a number of other things)
a lot of european countries (pretty much all the north) have it, mainly from russia fearmongering and "pulling their weight in NATO" to make up for not giving as much money to it as america would like (i.e. denmark gives the US intelligence, supports them in missions, and lets them use greenland for military bases)
short answer: being good little imperialist minions for the empire. it's random selection so around 10% of danes are picked