We consider ourselves as Egyptians and Arabs. Those are two mutually eligable "classifications" and not contradictory.
Our official name is the Arab Republic of Egypt. Some of the leading pan-Arab movements emerged in Egypt. Along with Syria and Iraq etc. Egypt has had an tremendous influence on Arabic culture from literature, music, cinema, cuisine to Islamic movements.
We are also located in the middle of the Arab world. Libya and the Maghreb to the West, Sudan to the South, Levant and Arabia to the East.
Most non-Arabs who embark upon learning Arabic learn Egyptian Arabic. Egypt is considered as the Mother of the Arabs among many Arabs as well. See post 346 for more detailed information.
In any case we are a diverse country and proud of this.