Why is Monetary Policy typically more effective at fighting inflation than unemployment?

They're pretty much the same method. Nobody goes around convincing employers to lay people off to fight inflation. Rather, when the fed slows the money supply, there is not enough money in the market to fuel the current rate of growth in the economy, causing a recession, and people lose their jobs. On the flip side, when the fed increases the money supply, there is too much money in the market, people spend more, and prices rise, meaning each dollar will buy less than it used to: inflation.