really is an arab because he is fluent in the language?

That makes no sense.


Where is this definition coming from?

Certainly not from the American English standard. Here's what Webster's has to say:

Main Entry: Ar·ab
Pronunciation: 'ar-&b, 'er-; dial also 'A-"rab
Function: noun
Etymology: Middle English, from Latin Arabus, Arabs, from Greek Arab-, Araps
Date: 14th century
1 a : a member of the Semitic people of the Arabian peninsula b : a member of an Arabic-speaking people
2 : ARABIAN HORSE

*****

So this must be the basis of your definition "a member of an Arabic-speaking people."

If that is the case than being an Arab DOES NOT mean someone who simply speak Arabic.