"Warum brauche ich eine Erlaubnis?"
Übersetzung:Why do I need permission?
As a native English (US) speaker, I might say "Why do I need a permit" (a piece of paper or a license indicating I have the authority or the right to do something), or "Why do I need permission" (the word permission is a lot looser than the word permit - it might be a physical piece of paper, or a verbal agreement, or even just an assumed understanding between two or more people) ... but right now I can't think of any instances where where I would say "Why do I need a permission" ... although I might say "Why do I need a permission slip?"
I'm not sure why "a permission" is not a good way to phrase it (assuming there's a grammar rule involved somewhere) - it's just that it sounds odd. I suspect that the reason might be that a permit or a permission slip is specific (a single object), while the word permission is more general (not really something that is quantifiable ... it's uncountable).
Re what KatinkaHes wrote below about the definition for Erlaubnis, when I look at Langescheidt it indicates Erlaubnis can mean either permission or a permit ... but like she says, my German is not good enough to be a judge there.
Ich hoffe das hilft!
Good question. It depends on what the Germain word 'Erlaubnis' means precisely (and my German isn't good enough to help). I can tell you the difference in English (roughly). A permit is more precise than permission. You need a permit to drive: an official statement to that effect.
In school children need permission to go to the bathroom, but it does not usually require a permit. A permit suggests that the government gave permission. The permission might be formalized through a piece of paper called a 'permission slip' though.