It's not a privately-owned institution. It's a central banking system with public and private components to it. The Federal Open Market Committee, who sets monetary policy, consists of the Board of Governors, who are appointed by the President and confirmed by the Senate, and the regional bank chairmen.
Questioning it is good. Believing in baseless conspiracies is counter-productive.
Where has it been for public for? Show proof that it is a public component...
Privately owned Institution just like the government of the U.S.
28 USC § 3002 - Definitions | LII / Legal Information Institute
United States means
(A) a Federal corporation;
(B) an agency, department, commission, board, or other entity of the United States