If I understand, taxes pay the Fed back, who previously "printed" all the money for the Treasury to fund the government.
Discussion
Yes, that's true. But that's actually paying for the expenses of the government. When money is created, it is balanced with debt. The Treasury creates the debts in the form of Bonds, Bills and Notes. Those are bought on the open market, and well, here is what the Federal Reserve website says about it:
How does the Federal Reserve's buying and selling of securities relate to the borrowing decisions of the federal government?
All monetary policy decisions of the Federal Reserve--including buying and selling securities--are made independently of the borrowing decisions of the federal government and are intended solely to fulfill the mandate set out for the Federal Reserve by law--maximum employment, stable prices, and moderate long-term interest rates.
The Federal Reserve purchases Treasury securities held by the public through a competitive bidding process. The Federal Reserve does not purchase new Treasury securities directly from the U.S. Treasury, and Federal Reserve purchases of Treasury securities from the public are not a means of financing the federal deficit.
In financing the federal deficit, the federal government borrows from the public by issuing Treasury securities, which are sold at auction according to a schedule that is published quarterly. The Treasury determines the types and amounts of Treasury securities sold at auction with the goal of achieving the lowest financing costs for the federal government over time. The Federal Reserve does not participate in competitive bidding at Treasury auctions, and the Treasury's debt management decisions are not influenced by the Federal Reserve's purchases of Treasury securities in secondary markets.
So, what I see here is a simple case of plausible deniability. But it still doesn't change the fact that taxes coming into the Treasury do go to pay down the debt held by the Federal Government, which while sold to the public through open auction, are bought by the Federal Reserve and then cashed in to the Treasury in exchange for the tax revenue that the Treasury receives.
According to the Treasury, the tax money the Federal Government collects is placed into the General Fund of the Treasury to pay for essential government services.
https://home.treasury.gov/subfooter/faqs/accounting-budget-faqs