It's worth pointing out that Asimov DID predict the increasing role of women in the economy.
Here's a quote from Asimov's speech on The Future of Humanity:
If we do have a very low birth rate, then what are we going to do with women?
Throughout history, the purpose and function of womankind has been to have lots of children. Now, no sane woman, if she came upon this whole thing cold, would want a lot of children; they're a lot of trouble, and they're dangerous to the health...
[group laughs moderately]
Seriously! When the germ theory finally came in and people learned how to arrange it so that women could have babies in reasonable safety, the world discovered to their surprise that women had a longer life expectancy than men. This had never been understood before, because throughout history women had, on the average, lived years and years less than men had. With all the dangers men faced, the hard work in the fields, the hunting accidents, the killings in war, everything else, women died faster for one reason and one reason only: childbirth. Every woman had one baby after another until one of them killed her. Usually, it didn't take long.
Well then, why do women do this? Because they are carefully told that being a wife and mother is the most glorious thing in the world, the one thing they're fit for, the most noble activity they can possibly have, and...and this is told to them until they believe it. And if they don't believe it, there's a lot of trouble made for them.
Well, I won't go into the whole thing. I suspect that you women know all about this already, and you men would rather not listen.
[group laughs mildly]
But notice the difference: once you want women not to have children, you're going to have to give them something else to do! It is absolutely impossible to tell a woman that she can't have children, and at the same time that she can't do anything else either except maybe wash an occasional dish.
[mild laugh from a few of the women in the group]
Because if you tell a woman that, she'll figure out some way to have a baby.
[swelling mild laughter from group]
I think I know the way, too!
[mild laughter from the group]
Well then, in the world of the 21st century in order to keep the birth rate down, we're going to have to give women interesting things to do that'll make them glad to stay out of the nursery. And the interesting things that I can think of that we give women to do are essentially the same as the interesting things that we give men to do. I mean we're going to have women help in running the government, and science, and industry...whatever there is to run in the 21st century. And what it amounts to is we're going to have to pretend...when I say "we", I mean men...we're going to have to pretend that women are people.
[group laughs]
And you know, pretending is a good thing because if you pretend long enough, you'll forget you're pretending and you'll begin to believe it.
[mild laugh from group]
In short, the 21st century, if we survive, will be a kind of women's lib world. And as a matter of fact, it will be a kind of people's lib world because, you know, sexism works bad both ways. If the women have some role which they must constantly fulfill whether they like it or not, men have some role which they would have to constantly fulfill whether they like it or not. And if you fix it so that women can do what suits them best, you can fix it so that men can do what suits them best too. And we'll have a world of people. And only incidentally will they be of opposite sexes instead of in every aspect of their life.
Why do Asimov's stories not reflect his own predictions? Well, it may be in part because they came a long time before this speech, but I don't think that's it. I've just read a collection of his, and back in
Hostess in the very early '50s he was writing about career women and the social problems they might face.
But the thing is: he was writing fiction, and for a particular audience. That audience were readers of popular pulp magazine stories in the 1940s and 1950s, and if he wrote some bizarro world in which women were people, the popular audience of his day would have rejected his stories as unbelievable, and/or communist. [he did write more prominent roles for women when he returned to fiction in the 80s, when the market would put up with it]
There was also an issue of what the audience demanded, as well as what it would reject. He said himself at one point that he rarely had prominent female characters in his stories, because he wasn't interested in writing romances - and back then, if you wrote a "women's story" (i.e. a story with women in it), you were writing mostly for a female audience, and that audience demanded romance and nothing but.
[I'm reminded of Doc Smith, when he wrote his first SF novel. His plot required there to be women, which meant there had to be a romance, but he wasn't interested in romance stories, so he had to find a female friend of his who would write the romance bits for him. A lot of the romance material was edited out in later editions, but you can still see its influence: Smith's SF plot required that his women be intelligent, strong-willed and independent; but the romance demanded that they get married, which meant a man had to propose to them, which could only be excused if it was obviously necessary for the woman's health... so every now and then a switch flips and the women become 'romantically' helpless and childlike and keep swooning, until eventually a man has to propose to them to calm them down... and then the switch flips again and they become strong-willed and independent again for a bit, and so on. It's interesting because in this case we can be confident it wasn't just Smith being misogynistic - he actually wrote them as more capable, and his female co-writer infantilised them because that's what the genre audience demanded...]
More generally, Asimov's approach to SF was generally, as it were, an experimenter's approach: change a variable, see what happens. He didn't set out to make full-rounded totally alien worlds every time he wrote a story - instead, his stories were mostly "1950s with a key variable changed", to see what effect that variable had. So, for example, in
Hostess, the story is just as much about Rose as an intelligent, ambitious woman caught between her career and her marriage as it is about the hay-eating alien medical researcher and the missing persons bureau, because in this story, gender roles are part of what the story is about. But in other stories, it wasn't, so he left things as they were, so that his audience understood his story more easily. In the same way, in one story about computers he might have a computer capable of doing all sorts of things, but in another story, about something else, he'd have the same things dealt with with slide-rules and the like - not because he didn't understand that computers could do these things, but because he understood as an author - rather than as a futurist - that presenting his readers with a world in which EVERYTHING was different, all at once, would alienate them and obscure his actual point...