First, because it's not the way actual day-to-day gender dynamics were, especially in the Lower and Middle Class. Modern historians of medieval Europe are finding that there's actually not a lot that women didn't do, when it came down to it, including being rulers and doctors and lawyers and warriors. Centuries of ignoring women's history have given people the impression that women didn't do anything that wasn't biologically based, but actually looking at the evidence when you don't make those assumptions is turning up some very nifty stuff indeed. What you think of as "realism" is really just a lot of rapidly-crumbling assumptions based on a bunch of dead white guys who monopolised the field for far too long.
Also -- lore reasons -- a lot of the sexism of the day was based on a patriarchal religious system where a woman was responsible for the fall of man and humanity. But Thedas has Christianity-as-founded-by-Joan-of-Arc. Matriarchal, woman-redeems-humanity. So if there's going to be that sort of morally based sexism, it's more likely to say "men are emotional, jealous, betraying bastards who can't be trusted with anything important." I'm pretty glad the writers have given that a wide berth, to be frank.
You want realism? Because class was at at least as important as gender, for starters, and class isn't even an issue in DA. Yes, you have nobles and peasants and an underclass and merchant bourgeoisie in the big cities and so on, but the actual day-to-day impact of class on the life of a medieval person is far greater than that of gender. A noble could cut a peasant down pretty much in cold blood as long as they had the blood price for that person's liege. A peasant could be told who to marry, where they were going to live, what job they would do, what crops they would grow, who they would fight and where and so on.
It'd make for a really different game though ...