I don't think anyone is claiming choice is the "entire effect" but I do think there is evidence that choice is the overwhelming effect. Let me ask this, do the women you know complain about an under-representation of women working at Discount Tire or in the field of Underwater Welding?
In America, during WWII a large number of women went into these types of occupations because of war time necessity and they showed they could perform the required duties just fine. But after the war most returned to traditional domestic roles. Are you saying that was not, by and large, their choice?