Oh, dzheremi! That's another can of worms
OK, here I go... We are Arabs in so far as we speak the language and are part of the Arab cultural milieu. I think its silly to argue otherwise, but yes, many Copts in the West do seem to resent being called "Arabs". I personally don't mind. I'm an Arab, I'm a Copt, and I'm an American. When I used to visit a local Antiochian Church which was a mixture of different ethnicities as well as many converts, by the end of coffee hour I'd usually wind up with the other Arabs; Syrian, Lebanese, Palestinian, even as my Arabic is quite broken. We just sort of click together in a unique way.
But you must also remember, this Arabness was forced on us. There was a time when to speak the Coptic language was to have your tongue literally cut off. And Egyptians were somewhat isolated compared to the Levantine Arabs. These nations of Syria, Lebanon, Palestine, Jordon, and Iraq as they appear today are all basically modern constructs of the Brits & French. Yes, there was a region of Syria or of Mesopotamia or of Lebanon, etc. But there were no hard borders and such, there was more free flow of people (with the possible exception of the Maronites and Assyrians who found safe haven in the mountains) among those regions for many hundreds of years. Whereas most Egyptians never left the Nile Valley until recently, mostly to the West for opportunities and the Gulf for work.
One last thought, the pan-Arabism I mentioned before can lead to the Pan-Islamism you mentioned and indeed has. But Egyptian Nationalism, call it Egyptian Arab Nationalism or whatever, has always been about the Copts and Muslims working together by it's very definition. Copts and moderate Muslims share the same goals for Egypt. The Islamists concern is for a return to the caliphate, this is not nationalism whatever they try to call it.