The Sahara is a desert because it is a desert. In the Sahel overgrazing can cause desertification, and parts of the middle east have been abused, I'm sure humans have made things worse in the Sahara, but it's a desert because that is how the climate of Earth works. Topography and location to water can alter this a bit, but generally speaking, deserts exist in and around 30 degrees of latitude north and south, plus or minus, for a reason. Too hard to explain here, below is a link to a great explanation. The Monsoons are pretty much the northern and southern extent of the Inter-Tropical Convergence Zone (ITCZ), which fluctuates between the deserts of the north and south with sun as direct rays migrate between the Tropic of Cancer and Capricorn. The ITCZ is what is responsible for tropical rainforests around the equator, plus or minus a few degrees. Can one green the desert? Yes, but it'll never be "wet". Rainfall could possibly be increased a bit, but the greening will still heavily rely on planned water conservation measures and not abusing the land.