To the extent that inflation is caused by an increase in money supply, it's caused by banks - not governments - creating too many loans.
Banks agree to owe money immediately to a borrower (creating the deposit), in return for being owed repayments in the future. This creates money and debt, by increasing the liabilities and assets on the bank's balance sheet. But the interesting thing is that the lending bank has to pay interest on the deposit that was just created, especially if the borrower spends the borrowed money
We therefore sometimes need to discourage banks from doing this, as too much lending will increase the money supply and cause inflation. To discourage this, the Fed increases interest rates, as banks don't want to create deposits on which they'll have to pay high interest.
Therefore, high interest rates are NOT something that is imposed on the government by the market.
High interest rates are imposed by the Fed on banks, to discourage the banks from their reckless inflation-causing tendencies
