That's because they want you to use a Nintendo network account, which are an individual thing. Simple solution, create another Nintendo network account, that way each player gets their own progress through the game.
I'm not saying the game is perfect, of course there's niggles that will need ironed out and I'm sure they will be.
But we also need to remember who's behind this game, Nintendo and as any long time Nintendo owner (I am one) will tell you, they've always been, shall we say, a bit behind the times since the modern connected world hit.
This is after all the company who tied a persons digital purchases to a device, not an account, a bloody device. So if your device broke, you lost all of your digital purchases unless you could argue with them long enough to restore them.
They aren't used to providing the sort of standard we, as Apple customers, are accustomed to receiving. But I'm prepared to give them the benefit of the doubt for now, I'm sure they'll get there sooner rather than later, they can't afford not to