Inflation => Interest rate hikes,

This path is not a given.
If inflation is caused by excessive money supply, raising interest rates (reducing money issuance) is helpful.
If inflation is due to supply shortages, raising interest rates is useless.
To put it simply, if printing too much money causes rice prices to rise, then raising interest rates and shrinking the balance sheet to pull money back will cause rice prices to fall.
If there is simply no rice, raising or lowering interest rates won't matter—people will still be unable to buy and go hungry.
Especially when oil prices rise, they can also affect factory profitability and suppress economic growth. In such cases, the Federal Reserve also has to consider another mission: stabilizing development and employment, which may actually require lowering interest rates.