The main meaning of 'jede' is 'each one'. If you say 'jede Katze', the image you have in mind is that you have the entirety of all cats in front of you and address each one in turn. Therefore you almost always (there are very few exceptions and they're very special) use the singular with 'jede'. You could also say 'Alle Katzen' for 'all cats'. http://www.duden.de/rechtschreibung/jeder

I believe that in English we make the distinction, but in German it is still a singular "cat" for the purpose of the sentence. So, we translate it as "all cats" but its more along the lines of "all cat" -- something we just don't say.