How is the money created by my auto loan a debt owed by the government to the Fed?
your hypothetical car loan was made possible only by incuring an initial debt to the federal reserve.
Initial money created by the Fed is only a small part of total money supply.
because your loan is backed up by a reserve of federal reserve notes and federal reserve notes only come into being via the sale of government debt instruments. Your loan is largely an illusion; however, the money they keep in reserves to keep their illusion from collapsing is real and it came into being as a result of the sale of US debt instruments by the US govt, debt instruments that will be paid for by the hard work of the US tax payers.
neither you nor anyone else could obtain a loan from a bank in any amount if federal reserve notes were not created, via the sale of debt instruments, at some point.