I can argue with anyone in the world except my wife. It's almost like I have selected mutism when she gets mad and I literally cannot say a word. Any advice?
When she says something, just repeat what she just said back to her. I know this sound counter-intuitive, but it is huge. I'll explain why in a minute. For example, if she says "you make me mad because you don't do this thing" say to her as calmly as you can "what I'm hearing you say is that I make you mad because I don't do this thing, is that right?" So matter what she says, mirror back to her what she just said. Allow her to tell you how she feels and just repeat back how she feels.
This is a skill. It takes practice, but it's easy to start just by repeating back what the other person said. The easiest way to start is to repeat word for word. As you get better, you can paraphrase. Stay calm. Let them correct you if that's not exactly what they intended to communicate.
This is huge because it lets the other person know you were listening and you got it. It seems rote to you, but to the other person, it's so wonderful! When someone does this to you, you'll see how absolutely wonderful it is to be listened to in this way.
You don't have to worry about what to say. Just repeat what she said. And she'll know you're really listening.