Why do Arabs call themselves Arabs?

Answer 1

The name "Arab" comes from the language that the tribesman spoke in what is now called the Arabian Peninsula. This language has been the defining aspect of Arab identity up to the present day.

Arab was not used in Ancient Times to connote an ethnicity or a common lineage. During the Age of Ignorance, Arabs commonly fought one another over religion, economics, social issues, and political power. The only unifying aspect of Arab culture was the use and reverence of The Eloquent Arabic Language (Al-Lugha Al-Arabiya Al-Fusha - اللغة العربية الفصحة) and a similar tribal lifestyle. (The equivalent in European terms would be if all of the White people who immigrated to Germany in the last 50 years and speak German at home would be considered ethnically German as opposed to splitting out the Spanish, Portuguese, Polish, etc immigrants as diverse ethnicities.)

As a result of this basis for identity, when the Arabs began to conquer previously non-Arab territories in the Northern Middle East and Northern Africa (Rise of Islam), they were able to "Arabize" (Ta'arib - تعريب) the native population (such as the Mesopotamians, Nabateans, Ancient Egyptians, Arameans, and similar such groups). They did this by teaching them them the Arabic, interbreeding with them, and building a more tribal structure than what was already there. (In most cases, the tribal structure already existed for the most part.) Therefore, by the late 1000s and early 1100s, most pre-Arab inhabitants of the Middle East had become Arabized.

Answer 2

In technical terms every where that you consider the middle east was Arabia. Hence where the term Arab comes.