Muslims claim that Ishmael is the ancestor of the Arabs. This however is contradicted by Ibn Ishaq's biography of Muhammad:
Ishmael is the son of Ibrahim (Abraham) b. Tarih (Azar) b. Nahur b. Sarugh b. Rau`u b. Falikh b. `Aybar b. Shalikh b. Arfakhshadh b. Sam (Shem) b. Nuh (Noah) (p. 3).
Then we have another line from Noah, where we read:
`Ad b. `Aus b. Iram b. Sam b. Nuh and Thamud and Jadis the two sons of `Abir b. Iram b. Sam b. Nuh, and Tasm and `Imlaq and Umayan the sons of Lawidh b. Sam b. Nuh are all Arabs. Nabit b. Isma`il begat Yashjub and the line runs: Ta`rub-Tayrah-Bahur-Muqawwan-Udad-`Adnan. (ibid. p. 4)
In other words, Ishmael's great-great-great-great...-great uncles were already the Arabs. This means that the notion that Ishmael is the progenitor of the Arabs is erroneous. At most, Ishmael can only be called an Arabicized Arab. That also mean that not all modern day Arabs are descendents of Abraham.
See also the discussion under ISHMAEL, and the article Who are the Arabs?