We're not both right when parent is saying the "federal reserve is lying about its mandate" - which makes no sense, not least because the mandate is defined, by Congress, in the Federal Reserve Act. The Fed's job is to execute on it. You can argue about their efficacy or tactics (in spite of their pretty solid ~110 year track record), but that's not the same thing.
It's like saying you think the USPS is lying that they have the mandate to deliver letters.