This isn't a "confusing paladin concept." Nothing in his request is about being a paladin and he has a weird request for it. He's flat out opposing your house rule of no evil characters, and has given you no other option, as a player, he doesn't get to just give you an ultimatum like "it's my only option." He needs to get with the program, whether he's trying to rationalize his evil or not, long and the short of it, he's a chaotic evil antipaladin, literally the divine representation of violence and selfishness in your no-evil party. Tell him he needs to rethink his character concept, or he needs to get packing.