It is to manage the money supply so that unstable prices don't hold the economy back. Unstable stock prices don't count, unless their instability threatens the larger economy. Whether stocks do threaten the economy is a much-debated question. So far, those who have predicted a big reverse-wealth effect have been disappointed. Spending on cars and houses has barely fallen at all, leading some to wonder whether Americans are as wired to Wall Street as all that.
Most people have a pretty good perspective on the market.
If falling stocks aren't threatening to tank the economy, then the Fed has less reason to worry about meeting Wall Street's expectations for rate cuts. Don't count on the Fed to bail you out. It's especially important given the heroic status that Greenspan achieved during the roaring bull-market days of the late 1990s. Whenever stocks hit an air pocket, it seemed the Fed was there, ready to sweeten the numbers. As a result, investors probably took bigger risks, and the stock-price bubble grew more than it might have if the Fed hadn't been so helpful.