The land of the Arabs historically was in Arabian peninsula south of Mesopotamia, that's why Sumerian texts refer to Arabs as foreigners and invaders.

The earliest known events in Arabian history are migrations from the peninsula into neighbouring areas. Around 3500 BC, Semitic-speaking peoples of Arabian origin migrated into the valley of the Tigris and Euphrates rivers in Mesopotamia, supplanted the Summerians, as the Akkadians (see Babylonia and Assyria). Some archeologists argue that another group of Semites left Arabia around 2500 BC during the Early Bronze Age Amorites and settled along the Levant mixing in with the local populations there. These Amorites eventually became the Arameans and Canaanites of later times Bernard Lewis mentions in his book The Arabs in History:

    "According to this, Arabia was originally a land of great fertility and the first home of the Semitic peoples. Through the millennia it has been undergoing a process of steady desiccation, a drying up of wealth and waterways and a spread of the desert at the expense of the cultivable land. The declining productivity of the peninsula, together with the increase in the number of the inhabitants, led to a series of crises of overpopulation and consequently to a recurring cycle of invasions of the neighbouring countries by the Semitic peoples of the peninsula. It was these crises that carried the Assyrians, Aramaeans, Canaanites (including the Phoenicians), and finally the Arabs themselves into the Fertile Crescent."

The Winckler-Caetani theory , named after its two most distinguished proponents, Hugo Winckler and Leone Caetani, which claims that Arabia was originally a land of great fertility and the first home of the semitic peoples. Through the millennia it has been undergoing a process of steady desiccation, a drying up of wealth and waterways and spread of the desert at the expenses of the cultivable land. The declining productivity of the peninsula, together with the increase in the number of the inhabitants, led to a series of crises of overpopulation and consequently to a recurring cycle of invasions of the neighbouring countries by the semitic peoples of the peninsula. It was these crises that carried the Assyrians, the Aramaeans, Canaanites (including the Phoenicians and Hebrews), and finally the Arabs themselves into the Fertile Crescent. The Arabs of history would thus be the undifferentiated residue after the great invasion of ancient history had taken place.

What caused the desertification? Climate change or agriculture?

I don't buy desertification as a cause of population crises.

This is very interesting (for me) topic. I always was fascinated by history of Fertile Crescent as The Bridge and origins of human civilisation.

Before we start I would like anybody who likes to seriously discuss this to have a look at this website

Abraham was from Ur, which was Sumerian city state.

war with never ending waves of newcomers and politics of it all made Abraham's extended family-tribe Hebrews

They started to live as nomads amongst nomads and Hebrew language gradually become Semitic language

That's why ancient Hebrews and Arabs had different but not 100% "racial" futures but similar languages.

The Sumerians were a non-Semitic people and were at one time believed to have been invaders, as a number of linguists believed they could detect a substrate language beneath Sumerian. However, the archaeological record shows clear uninterrupted cultural continuity from the time of the Early Ubaid period (5300 – 4700 BC C-14) settlements in southern Mesopotamia. The Sumerian people who settled here farmed the lands in this region that were made fertile by silt deposited by the Tigris and the Euphrates rivers.

Despite the lack of corroborating written records, it is generally agreed that Sumerian speakers were farmers who moved down from

the north

, after perfecting irrigation agriculture there. The Ubaid pottery of southern Mesopotamia has been connected via Choga Mami Transitional ware to the pottery of the Samarra period culture (c. 5700 – 4900 BC C-14) in the north, who were the first to practice a primitive form of irrigation agriculture along the middle Tigris River and its tributaries. The connection is most clearly seen at Tell Awayli (Oueilli, Oueili) near Larsa, excavated by the French in the 1980s, where 8 levels yielded pre-Ubaid pottery resembling Samarran ware. Farming peoples spread down into southern Mesopotamia because they had developed a temple-centered social organization for mobilizing labor and technology for water control, enabling them to survive and prosper in a difficult environment.

I'd be more inclined to accept they came from the south than the north, since they were originally called sag-giga, literally meaning "the black-headed people", due to the fact they were black skinned.