I'm probably projecting my own experiences onto your wife, but I always get annoyed with people who hear something like "be dispassionate and try to be as logical as possible" and immediately discount it- primarily because I notice they've never tried it.
I used to make a lot of emotional decisions based on my gut feelings and intuition, and it took me a great deal of work to get over that and to start thinking about the "optimal course of action" whenever I had important decisions to make. My life has drastically improved, and all of my relationships are more stable and my goals have proved to be more attainable.
But when I try to preach this to people, a lot of them give the same reaction your wife did- and I get annoyed, because I observe them constantly having their feelings hurt, getting frustrated, missing their goals, and feeling stressed out, because they're operating off of anything but "optimal course of action reasoning".