He isn't just taking your body. He's taking your life.
Ring is about the sweetest guy that has ever worked outside the system, aside from the murders and the drinking. He can't remember who he used to be, but he knows what he has to do. He is a ringer, after all.
Although the friendship that he shares with Henry is like nothing he has ever known, Ring must take his life before the old year becomes the new year. The more Henry comes to accept his fate, the more Ring rails against his own.
When he takes Henry's body, all of Ring's memories will be lost forever. He can't remember an assignment ever being so hard to complete.
Then again, he can't remember much of anything.