I've seen many women in the European upper class or aristocracy wear scarfs like that.
Christine Lagarde comes to mind as do Susanne Klatten etc.
I don't know why it looks weird, but I bet they think it looks stylish.
Until I was in my twenties, I thought that's the only way to wear the scarf on women.
But to my defence, that's the traditional way of wearing the scarf (selendang) in my country, when paired with the kebaya or kurung. (but come to think of it, historically, the ladies might be copying the western women, or vice-versa?)