How would you use neither...nor when articles are involved? For instance: "My pet was neither a cat nor a dog." It sounds better to say "My pet was neither green nor blue" than "neither a...or a..." so I was wondering if there was some rule about this? Regarding the first example, "My pet was neither a cat or a dog" sounds more natural to me, for some reason.
As @Edwin Ashworth says, we need some context. This is always needed because English is a context-dependent language.
Neither a P nor a Q
John: Do you have any pets?
Mary: I have one pet.
John: Let me guess. I bet it's a dog or a cat.
Mary: No it's neither a cat nor a dog. (This refers to a specific individual)
John: Is it a rabbit?
Neither P nor Q
Mary: My goodness! What kind of animal is that?
John: I don't know. It looks weird.
Mary: All I can say is it's neither cat nor dog. (This refers to the species)
John: I think it is some kind of predator whatever it is.