"Arab" is a bit of an odd word in English. I would only ever say "Tamer is AN Arab," because I have only ever heard the word used as a noun. For the language, of course, I would say "Arabic," as in "Tamer is an Arabic translator." For some other things, I would use "Arabian," as in "Arabian cuisine," but I think that would really only apply to the cuisine of the Arabian Peninsula. I would never say a person is "Arab," but then I would not say a person was "Arabic" or "Arabian" either (unless the word Saudi came right before it), only ever that he was "an Arab." We have a few other very old ethnonyms like that, such as "Turk" and "Jew," though even in those cases, we are more likely to use the adjectives "Turkish" and "Jewish" do describe the people, possibly because the former describes a nationality and the latter a religious identity.
Perhaps it's a regional thing? I, as an English speaker, wouldn't say someone is an ( insert ethnicity). To me its sounds wonky to say 'is an Arab'. To me 'Omar is Arab' sounds, and feels correct. Though, I'm sure both technically are correct and mean the same thing.
I think many people are very nervous using ethnic terms with which they are unfamiliar, for fear they will offend. I taught at a school with, as far as I could tell, no Jewish students, for instance, and some of my students thought the term Jew might be offensive. Of course, I pointed out that I studied at a school with many Jews, who all used the term of themselves and preferred others to use it of them. At that school, there were many students who were Arabs, who also used that term to describe themselves, when they were speaking English. Turks, Swedes, Mongols, Britons, and Danes are others who seem perfectly happy to be described with such a noun.
The commenters are right. "Omar is Arab" does not make sense. "Omar is an Arab" is grammatical but might be rude.
It was certainly not considered rude by my Arab students. They may simply have grown used to our Midwestern American usage, though, I guess.
The real question is: is this the correct and commonly used Arabic expression. I also find the English form a bit strange, but in this course it is about learning Arabic.