But if you listen to the women who have had bad experiences with male providers, it's not usually about competence. It's very rarely "this male doctor missed my diagnosis because he doesn't know what endometriosis is, and therefore I'd rather see women from here on out." It's
"this male doctor missed my diagnosis because he didn't listen to me, didn't believe me, etc., and I think that women are less likely to do those things." It's typically about communication style, and there is PLENTY of data to support differences in communication style between men and women, some of which has been done on physicians. There are also lots of studies out there showing that physicians do a bad job of taking the complaints of women & people of color seriously, and maybe people feel like if they see a doctor who is like them, they have a better shot at achieving their health-related goals. Maybe that's true, maybe it's not, but it's not an irrational assumption - the data backs it up (see
this recent study showing that women who came to the ED with an MI had slightly improved survival rates when treated by female physicians, or even in EDs who hired a higher proportion of female physicians).