First of all, it is impossible to have stagflation without a shift of the short run aggregate supply (SRAS) curve to the left. Stagflation consists of higher inflation along with higher unemployment. It is impossible to get this without a decrease in aggregate supply. Inflation can occur if the aggregate demand curve shifts right/up and high unemployment can be caused if it shifts left/down, but high unemployment and inflation cannot exist at the same time unless the SRAS moves to the left. Therefore, we can say that the SRAS moves to the left in stagflation because stagflation cannot occur unless it does.
But why does the SRAS move to the left? The most typical answer for this is that supply shocks cause the SRAS to move to the left. A supply shock is an event that directly affects the amount that it costs businesses to produce their goods and services. Higher costs tend to reduce supply, which makes the SRAS shift to the left. The most famous example of a supply shock was OPEC’s decision in 1974 to curtail production of oil, thus causing the world price of oil to jump rapidly and dramatically. This raised the costs of production for essentially every firm in the United States, moving the SRAS to the left and causing stagflation. Thus, we can also say that supply shocks cause the SRAS to move to the left during stagflation.