At first, Say's Law may seem 'obvious'. Though, it's not - actually, it's highly controversial. The reason it may seem obvious is that you have perhaps learned from microeconomics that in equilibrium, demand is equal to supply. If you're outside equilibrium, prices will adjust and you shall be taken back to equilibrium.
This isn't the motivation behind Say's Law which isn't an equilibrium condition. In the classical model, YS and YD are real variables which don't depend on the price level. This may strike you as odd. YS relies only directly on L and K and indirectly on the real wage. If price level increases in the classical model, wage level will increase by the same amount leaving the real wage unchanged. As for aggregate demand, if price level and wage level both increase (by the same amount), there is actually no change for the consumers. If all prices double whereas you income doubles, there is no need to adjust you demand.
The justification for Say's Law isn't as an equilibrium condition through price adjustments. No price adjustment in the world would equilibrate aggregate demand and aggregate supply in the classical model. In its place, justification is based on income effects instead of on price effects: higher supply Þ higher income Þ higher demand.
The reason why Say's law is so controversial is following. Assume that investors and consumers fear that the economy will slow down. They may then decide to save a substantial part of their income and aggregate demand may not be equal to aggregate supply.