Reducing inflation by raising interest rates makes money more expensive, which hurts those that need to borrow it and benefits those that can lend it. Higher rates also make assets cheaper to buy as less leverage can be brought to bear in bidding. Anyways, the fed should have raised rates when the economy was good (and not just good because money was cheaper), so they could reduce them when the economy was bad. These days, we are all just addicted to cheap money and all fiscal discipline has been thrown out the window (cut rates in bad times and good!).
The economy hasn't been good anytime recently until 2019 or so. Unemployment consistently improved over time far past any mainline economists predicted, especially the Larry Summers types who ran the 2010 recovery. Maybe they should've lowered the rates then so they could raise it later - they certainly didn't do enough stimulus.
There are weak models behind all of this at best; "cheap money and fiscal discipline" isn't even a model, just moralizing, but the actual arguments about fiscal policy use things like "potential output", which has assumptions like "the economy will overheat if black people have under 10% unemployment".
As for current inflation, it's not yet enough to ruin the Fed's decades long record of undershooting the 2% target, but it is caused by an ongoing natural disaster and not money printing. So to fix it, you can try fixing the natural disaster…
Even in 2019, Trump pressured the Fed into not raising interest rates, saying they would make the economy crash. Trump is hardly alone in blame, Obama, Biden, and Bush are just as bad.
Money has been cheap since 2008. Did everyone expect it to be cheap forever without consequences? COVID just blew down a house of cards, fixing COVID isn’t going to magically fix our inflation problems, the house has already been blown down and it will take another decade of fiscal discipline to build something sturdy back up again.
It should be possible to achieve better employment without punishing savers and rewarding debtors.
