The reason is simple: incoming refugees will cause internal strife and fracture the Saudi Royal family's tenuous hold on power. I don't agree or disagree with that premise, but that's the reasoning.
The same is occurring in Europe and even America. The establishment is threatened as a result of this mass immigration. Perhaps the difference is that the Saudis do not suffer from white guilt and, hence, attempts at rational discourse are not drown out with calls of racism, Islamophobia, and xenophobia.