why Abraham took the long way to the western cities of Shechem, Hebron, and Beersheba instead of just traveling west through the Arabian Desert.

Abraham maybe chose the longer way to get to his desired destinations, but he for sure chose the safer way to them. He chose the longer way because of the harsh conditions of the Arabian desert. It is a vast, hostile desert, where sandstorms are very common and deadly, and food and water are almost impossible to find. Also, on the Arabian Peninsula, in this period of time, there was still and active chain of volcanoes, so traveling through the desert was pretty much suicide.