As a world-class introvert, I have to say that is not an introvert/extrovert problem. The man is accusing you of trying to spy on him because he has something to hide. You're just being considerate, doing what any normal spouse would do in asking about his day, trying to connect - he is on the defensive because he feels guilty. If he didn't feel guilty or have something to hide, he wouldn't be lashing out at you.
I strongly recommend that you take measures to protect yourself and any children involved in the relationship. THEN, when you know that you're in a strong position, insist on counseling, or find a way to find out what he's hiding.