That's because the actual way to lower inflation, raising taxes (especially on the ones who have most of the money), is deeply unpopular with the people who control the government (the ones who have most of the money). Also, everyone likes to pretend the government has a "budget" that equals the taxes it brings in, rather than taxes and spending being the mechanism by which we can control inflation and the tool to improve the economy. That isn't the narrative they've been writing all these years.

Literally, the fed increasing rates means they want to make more people unemployed, because they think inflation is caused by workers spending too much of their expendable income.

That's not what they think, it's just the only tool the Fed has left at this point to try to lessen the overall impact of inflation. They can't raise taxes. They can't end Trump's stupid fucking wars. Those are all functions of Congress doing their fucking jobs.

That's not exactly right. Any economist would correct you.

When money becomes more expensive to borrow through higher interest rates, it results in everyone taking out less debt (at least in theory), so the total money supply is lower (because a new loan is new money in the economy), and less money chasing the same goods means the value of the money increases.

It doesn't have to be businesses taking out loans for capital from banks (other debt instruments such as bonds only move money from investors to debtors without changing the money supply), it can also be individuals buying homes or racking up credit cards or taking out auto loans. All the money is the same, created through debt.

And reducing the money supply can and does work. The effect on employment is real. Imagine if you have a company that sells milk shakes. When people have lots of access to cheap debt, there's lots of dollars so lots of people can come buy a milk shake. And you might hire more people because you're selling more milk shakes, and with so many customers you can afford to raise prices. If they can't take out cheap debt, fewer people come around, you have to fire people because there's no work for them, and you won't want to raise prices, you might even need to lower them. Therefore, unemployment is an expected result, but not the desired one. The desired result is fewer dollars than the base case.

This is because of how money is created in our system: when you put a dollar in the bank, the bank can lend out multiple dollars. Presently the Federal reserve has a 0% reserve ratio, so banks can lend out infinity dollars for every dollar they have, only limited by liquidity, funding, risk management, and creditworthy borrowers. In a system without fractional reserve banking where you need a dollar to lend a dollar, absent other forms of money creation such as minting, the money supply would not grow and would be more likely to shrink, and prices would be likely to stay stable or drop.