Deforestation is a common cause of desertification worldwide. Trees help to capture moisture from the air and bring it to ground. Cut them down, and the moist air blows past. Trees are commonly cleared for farmland, and then the farmland has to be abandoned when it gets too dry.
In the Amazon basin and along the northwest coast of North America, trees were the basis of productive agriculture, carefully chosen mixes of trees of different sizes and species. To this day the Amazon basin is dominated by tree species that were once cultivated throughout, supporting tens of millions until they were wiped out by smallpox and other pandemics. In North America, such tree gardens can still be found centuries after they were abandoned.
Trees alone do not help. There are a lot of tree farms which do not capture moisture and are prone to forest fires. We need forests with good ecosystems not tree plantations.
2. The Euphrates floodplain is still quite green, like the Nile's. It's not like the US midwest where you have thousands of square miles of grass, but you do have a strip of extremely reliably fertile land (and for civilization-building, reliable seasons are super important).