The reason why the Fed would follow a contractionary monetary policy is because they feel that inflation is a problem or that it might soon become a problem if it is not checked.
The Fed wants to keep the economy expanding, but it does not want the economy to “overheat.” If the economy starts to have inflation rates that are too high, it can be bad for business. Banks, for example, can become apprehensive and less willing to lend money if inflation is likely to be high. They will raise interest rates, which might decrease borrowing, for example.
For this sort of reason, the Fed sometimes follows a contractionary monetary policy. In times when inflation is a threat, they try to reduce the money supply. If the supply of money is reduced, aggregate demand will typically drop, or will at least not rise as fast. If the rise in aggregate demand slows, so will the rise in the price level. A contractionary monetary policy, then, is used to prevent inflation because inflation can, if it is too high, do serious harm to an economy.