It's very tricky, because it takes about six months for the effects of monetary policy to trickle through the economy. They can misread economic data, like the Federal Reserve did in 2006. The Fed thought the subprime mortgage meltdown would be restricted to housing, and waited to lower the Fed funds rate. By the time the Fed realized the slowdown was infiltrating the entire economy, it lowered the rate quickly - but it was already too late.
On the other hand, if central banks stimulate the economy too much, they can trigger inflation. Central banks avoid inflation like the plague. Ongoing inflation destroys any benefits of growth by raising prices, and costs, and eating up any profits. Therefore, central banks work hard to be sure to keep rates high enough to prevent it.
Politicians and sometimes the general public are suspicious of central banks because they usually operate independently of elected officials. They often are unpopular in their attempt to heal the economy. For example, Federal Reserve Chairman Paul Volcker raised interest rates to curb runaway inflation - and was bitterly criticized for it. Central bank actions are often not well understood, which raises the level of suspicion.They could really benefit from a top-notch PR agency!