"I wish there was a way to convince him." Eddie didn't care much for sharing his things either. Even when it came to his daughter. Much less his husband.
Whatever it took, Edward would do it. Scarecrow was part of Jonathan, the man Eddie would end his life for, and they couldn't hate each other forever. Well, they probably could but Eddie didn't want to.
It was counterproductive. And Eddie was far too selfish for that.