Suppose one doesn't want to allow the vacuum of "you are not a boy" to exist. How important is it to fill this with positive stereotypes? Even ones which are slight misreadings or spins of current ideas. E.g. of course you would want to be a scientist as everyone knows women have the capability for those all-important intuitive flashes which all great scientists need, but can't be taught. Or depending on your family -- e.g. for expats, Well honey, of course you're the best in your class in physics, Newton was English, or The women in our tradition/culture/city have always had special gifts, or even, Yes I can tell she takes after her grandmother, she's going to be an outstanding diplomat. Anything to latch onto.
It's complicated, of course, but I think this is one of the major problems with the modern philosophy of equality in everything. When it is layered onto deep-set societal beliefs that men are attributed the positive qualities and women get the reflected light, it is not enough to give most women a positive sense of self and an appreciation of their gifts as being uniquely theirs (not as women, of course, but as human beings).