"Fed independence" doesn't mean the Fed answers to no one — it reports to Congress and operates under a legal mandate set by Congress — it specifically means the Fed is structurally designed to make individual monetary policy decisions without day-to-day political direction from the President or Congress. The economic case for this design rests on a real, formally studied idea called the "time-inconsistency problem": politicians facing elections have a real, understandable incentive to prefer looser monetary policy (lower rates, more stimulus) for a short-term economic boost, even when that comes at the cost of worse inflation later, after the votes are already counted. An independent central bank, insulated from that specific incentive, is theoretically better positioned to make decisions based on longer-term economic health rather than the next election cycle.
This isn't just an abstract theory — economists Finn Kydland and Edward Prescott were awarded the 2004 Nobel Memorial Prize in Economic Sciences partly for formalizing exactly this problem, building on a foundational 1977 paper making the case for policy rules and independent institutions over politically-driven discretion.
Correct moves you up, wrong moves you down — reach 100 to master this lesson.