Someone being a professional debater is neither here nor there. Hardly anyone comes home and does their day job with their spouse.Of course not. He's a professional debater, and so she must know that it's a waste of time.
As you yourself note, he's basically a prick. This is him being a prick in a domestic situation. The way he "debates" in his day job derives from him being a prick.
No. The core of the argument is simply that she wants to leave the house and he doesn't want her to.She doesn't want Steven to tell her how to do things despite describing mundane problems that are rather easily solved.