Don't let your stubbornness keep you from dealing honestly with your stubbornness! And don't excuse it or conclude you can't (or won't) do anything about it, because God wants to help you overcome it -- both for your sake and the sake of those around you.
What's wrong with a stubborn, unyielding attitude that always insists it must be right? For one thing, it comes from pride -- the kind of pride that refuses to see another person's point of view, and is blind to our own faults. But this kind of pride is a sin in God's eyes, and it leads inevitably to His judgment. The Bible says, "I hate pride and arrogance, evil behavior and perverse speech" (Proverbs 8:13).
A prideful, stubborn attitude also cuts us off from other people, and ultimately from God. Who likes to be around someone who never listens to advice and claims they alone are right? Probably no one -- and when you get two stubborn people together, the sparks begin to fly. The Bible warns, "Pride only breeds quarrels, but wisdom is found in those who take advice" (Proverbs 13:10).
Face honestly your wife's criticism, and ask God to help you see yourself the way He sees you. Then submit your life -- including your pride -- without reserve to Jesus Christ, and ask Him to forgive your sins and help you to be more sensitive to His will, as well as the feelings of others.