Why raise rates in a slowing economy?

It is quite obvious that the price of oil is up significantly and that the cost affects many different aspects of the economy. Prices for all types of items are increased. Many inputs like fertilizer, plastics, heating and cool along with transportation and on and on are more expensive.

All this means that the economy will slow because peoples' income can not adjust near a quickly as the prices increase.

So, knowing that indexes like CPI will rise as these costs move through the economy, why would people at the Fed want to raise rates? There isn't a shortage of oil, so the goal of slowing demand may have an effect on lowering prices, but it will make the economy much worse.

When there was too much cash in the system causing too much demand, it made sense (to me) to raise rates to slow demand. Now demand is falling… Why wouldn't you lower rates to lessen the burden?