Something else that isn't mentioned is that Arab is an assimilationist identity, IE anyone can become an Arab, just like anyone can be considered American. The conditions vary, but if a person lives in an 'Arab' country for a long time, learns and speaks Arabic, and embraces Arabic culture they will become an Arab. So it isn't quite an ethnic group as ethnicity usually requires shared origins.
^This. An example is that my Dad looks more like your average Eritrean/Somalian guy but is supposedly considered as 'Arab' as my Egyptian mum, just because he speaks the language. Anyway Arab is an ethnicity which spans a broad range of people, just like Latina/Latino.
But yeah I've noted that some Arabs, especially gulf Arabs (Saudis in particular) tend to have that 'chosen ones' way of thinking and look at all other Muslims as people who merely 'adopted' their religion. Personally, I refuse to label myself as an 'Arab', or anything else for that matter. I speak the language, yes but I don't identify with any particular aspect of it, save for Koshari and Shisha.