The New York Times distinguishes between being compatible and being complementary.
Amy Sohn wties (excerpt):
At the time I was seeing a 92-year-old Austrian psychoanalyst, and whenever I expressed concern about the financial inequity of my relationship, he would shake his head and say, “For the relationship to survive, you must be the woman, not the man.”
Later I switched to a Buddhist psychiatrist in his 50s, and he said: “Sounds like it works. Someone’s got to do the cooking and house care. Be grateful you met a guy who can.”