People who hold tightly to the right to be right can go to just about any length to prove they are right, even to the point of ending the relationship. Give up the right to be right. Check out what you might be able to learn from the other point of view, which might even be as valid as your own. Shocking, I realize, but highly possible. The simple truth is that in marriage there are times when you can be right or be happy, but not both.
Conflict arises and they shut down.
And, they're more than willing to remind you, in detail. Write the current conflict on the blank board. Deal with it. Over, done with, gone. I'm guessing that you have identified your partner's style of conflict.