I wanted to discuss this with someone for a while now, Furuya Rei is a good character who loves is country and ready to sacrifice his life for anyone who needs help and he does his best to provide information about the BO to the secret police department he works at, but he was ready to hand in Akai Shuuchi to the organisation he even told Vermouth about Conan's plan and it's all due to Vermouth being too scared to believe that Akai is alive and luck that the black organisation didn't know about Akai's fake death.
Akai is known as the Silver bullet in the organisation and everyone of the BO code-named members know about him and is scared of him (except Gin) even the BO's boss and yet Rei was going to hand him over to the black organisation.