The biggest issues are the fact that it's inflationary and debt-based. It's also controlled by those with political connections and used as a political tool.
Most central banks are generally independent from political affiliation and are not controlled by any political appointee.
The Federal Reserve was created by an act of Congress and the president appoints the Fed Chairman. Also, a significant amount of the federal government's funding has been coming from the Fed.
The president appoints the chairman of the federal reserve (as well as each of the member of the board of governors of the fed) however there is no accountability to the president once they are confirmed by the senate. Also the federal reserve does not receive any funding from the government (it is the other way around) so it is not subject to congressional pressure