I don't get how Liverpool fans should be mad at him, the guy's reputation has been on a decline for half a decade, this is probably his last train if he wants to coach at the top level and surely Liverpool would never offer him a job after his last stints due to his "Legend status", I don't know why Rafa should skip the best offer he'll probably get for the rest of his life just to save face for a club that wouldn't consider hiring him in the future.
I could understand it from the Everton point of view, some die hard fans may even consider that it's better to be relegated than to be coached by Benitez, but at the end of the day no president wants to risk that.