IMO the best thing to do is to ignore the person when they are pouting and giving the silent treatment. Think back to when you were a child; the silent treatment was only fun/satisfying when it bothered the other person. He wants you to go out of your way to get him to talk, he wants you to beg him to forgive him and to please talk to him.
When I would get the silent treatment I would enjoy the peace. It was nice to be able to hear myself think and not have to listen to the addict go on and on about themselves. Luckily, I don't have to deal with that anymore.
Keep working on you. Maybe after him giving you the silent treatment long enough you will notice that you could be happy on your own. It's weird how much you can come to realize in a week or two of not hearing the constant background noise and quacking of the A.