You said that A) the Fed was created to provide loans to banks, B) the Fed was not loaning enough to banks during the Great Depression. That hardly sounds like a rational argument against the Fed's existence. That sounds like you want to out-Fed the Fed. And I would agree. They didn't expand the money supply NEARLY enough during the Depression, which certainly exacerbated the problem.
What it sounds like is that you're choosing to ignore all of what was said except those parts you feel implies an inconsistency in a philosophy you're not capable of understanding, and meanwhile, you're refusing to grasp the gestalt of what was said.
How do you then conclude that the Depression could not have happened without the Fed? You stated that the economy was worse because the Fed wasn't loaning money to banks and allowed them to collapse. If the Fed hadn't existed (and thus, there had been no one to fulfill the objective of loaning money to banks, as you stated), how would the economy be better off?
See what I mean? Did I not say that regional failures may have occured on the sector level? Did you miss that part? That's what normally happens in recessions. The Federal Reserve managed to turn a regular old recession into the worst economic disaster in history. ONLY the Fed was able to make the nation's entire economy collapse.