I've really got to agree with this one. I can be fine with evil characters, because even evil characters can have friends. I really dislike campaigns where a player is trying to compete with the GM to be the party's great antagonist.
That said, if nothing has come up in character yet, then it may be an empty threat. Or alternately, I suppose he might try to kill a paladin, but not your paladin. I've had players/characters who have a stated hatred of all paladins, with the exception of the party paladin. "Oh Steve? Yeah, he's got a bit of a stick up his butt, but he's all right."