It is because most of the winds flow there which makes it sandy and also the wing that wind is hot . Hence making it a desert.
1 Trade winds that blow in the region shed their moisture on the eastern side.They become dry by the time they reach the western margin of the continent.
2 Cold ocean currents also help in the formation of deserts as they do not cause rain ,mist fog lower the temperature.
3 As these deserts lie in the subtropical high pressure belts they are associated with sinking air currents which do not help in rain.
4 In most of the cases mountains r present on the western side of the continent which do not allow wind to shed moisture in the west