I hired a GC to build my house so he could supervise and handle subs and get materials. When he tried to charge $32,000 for the finish carpenter and I got several bids for $20,000, I hired my finish carpenter. I ended up hiring someone else to finish much of the interior and the Masonry both inside and out. He gave me credit for the amount on the cost breakdown, but since he didn't do the hiring, scheduling or supervise, should he also give me credit for not doing those things and that should reduce the amount on the contract?
It depends on what is in your contract. Most GC's include in thier contracts a provision allowing them to charge for supervision of subs the owner hires directly, so I would review your contract--or have an attorney review it-- to see whether he is entitled to charge you.