Do all kurds speak Arabic

No, not all Arabs speak Arabic, however. If these Arabs live in an Arab country they will speak Arabic. Many Arab Americans do not speak Arabic. Being Arab is an ethnicity, who all descend from Arabia or the Levant. There are also different cultures like Sudanese people who are considered Arab, because they are apart of the Arab League of Countries, whose national language is Arabic. To clear up to you the facts, the only real Arab people are people who descend from Ismail(Ishmael), the son of Ibrahim(Abraham) and Hajjar.