The Fed's stagflation fear

Here is an article explaining the negative of reducing rates to help the economy. There is only so much a rate cut can do. What can happen is that inflation can take over and the economy won't recover. The average person is stuck in a place where things cost more and the economy is poor, so no new money will reach them. How can the economy recover if the average consumer is spending more money on gas, groceries and other essentials. The average person is left with little or no money to buy consumer goods. When the fed doesn't care about inflation and it is a real thing then the economy has no chance to recover because all of the limited spending in an economic slowdown goes to essentials. (The Fed's stagflation fear)