The Federal Reserve is supposed to have independence from the government. It will develop its own monetary policy which doesn't need government approval. In reality, the President appoints all the Governors, so people get selected based on doing what the President wants done.
The Fed's monetary policy is typically an inflation target - keep the money supply growing to encourage growth, but keep inflation in check as well.
The problem is the political influence starts to impact the pure decisions about what's best for the economy. Election coming up? Well, hold off on increasing rates since we need good employment numbers for the next few months.
If the economy gets unstable the Fed ends up riding the razor's edge trying to stick to policy but not piss off the President. Problem is that the economy can go off the rails faster than the Fed can response.
The issue highlighted after 2008 was that "yeah, printing new dollars and buying distressed assets worked pretty well! and no massive inflation so far. But there will be incredible pressure to not raise rates later and if the Fed waits too long to apply the brakes, they won't be able to get ahead of it and inflation will skyrocket."