When marriage therapist Sharon Gilchrest O'Neill met with new clients recently, she asked them why they were seeking therapy. The couple told her they'd spent years arguing over finances and recently had their worst-ever blowup. The husband complained about how much money his wife was spending; the wife said her husband was controlling. They hadn't slept in the same room for months.

Ms. O'Neill, whose practice is in Mount Kisco, N.Y., then asked the question she often poses in a couple's first session of marriage therapy:...