That and the fact that the current government hardly classifies and 'conservative' in any meaningful international comparison. At best they're a "slightly less socialist" government.
To be fair, they have to have some (arbitrary) name for the coalitions.
The semantics of political parties and ideologies are one of the most confusing things. Both the Democratic and Republican party are to the right of most, if not all, Scandinavian political parties.
In a system with more than two parties, you have to name your party something that actually connotates the party's policies (Democrats and Republicans doesn't exactly mean anything to outsiders), and considering that many of these parties have existed for over 100 years, their policies have obviously changed since they got their names. (This makes it pretty awkward for the parties who deviate from their historic names. Consider the parties that were created when Communism was all the rave, but are still around. They need to distance themselves from the past without denouncing their party's raison d'etre. I'm sure that's why we have so many nebulous party names cropping up: "Freedom", "People's" parties and whatnot.)
You often hear people refer to American policians as liberal, progressive, conservative, libertarian and so forth, which are ideologies more so than something reflected by the party names. Democrats can also be conservative (Blue Dogs), and so on and so forth.
In a system that isn't (basically) a two-party system, people use their party name to characterize their policy: "Social-democratic, moderate, conservative, socialist, liberal, (which means something akin to libertarian on that side of the Atlantic)" as using other attribute would be a denouncement. Instead, silly buzz words like "welfare", "freedom", "fair", "tough", "rewarding", "equality", "Danish", "Swedish", "Norwegian", etc. crop up to frame their policies. This makes it an enormous clusterfuck to get a grasp of the - actual - politics in a political environment where basically all the parties are social-liberal.
You have to find some word to delineate the coalitions from each other, and there isn't any great way to do this. Sometimes, you use colours for the coalitions, but these make no sense to outsiders. (The left coalition in Denmark is red and the right blue, whereas Democrats are blue and the Republicans red. Is your head exploding yet?)
You're probably wasting your time. The US has its own Steve Jobs-esque distortion field when it comes to politics. I'm not sure the majority of them could ever be educated what "left" and "right" actually mean and you'll certainly never convince them that both their main political parties are actually center right and far right.
This "distortion field" sounds suspiciously like relativity. Are you sure you aren't just declaring your political sphere the center of the universe and labeling anyone who uses a different reference point as a heretic?
Wait, what? I'm declaring the rest of the world the "center of the universe" and labeling the one (first world) place that uses a drastically different reference point as wrong.
It is relativity, but the problem is that most people here don't understand that the parties are center right and far right relative to most other developed countries.
What does that have to do with the state of welfare? If anything economics is usually used as a justification for not having a very inclusive welfare system.