I think that I read more stories where authors say a woman is trying to change a man. I have no idea if this means anything about reality. But the myth is that men are the “beast” and they need civilizing, and women are the ones to do that. I think that in stories, they are generally successful.
So a man has raw talent, but needs a woman to channel that talent. She gives him motivation to make money or to go to school so he can get the skills he needs to make money and take care of the family, etc. The woman is more organized and can therefore make a plan and tell the man what to do. He doesn’t have to think these things through any more. That’s one myth, anyway.
Then there’s the Pygmalian myth, where the man finds a diamond in the rough and educates her and civilizes her and then, of course, falls in love with her. This is a class thing, where the man is upper class and the woman is working class, and he raises her up to the upper class.
Then there are the codependency issues. A man and a woman are so wrapped up in each other, and they imagine the other will somehow be perfect if only they would do this or that. A woman might think she could rescue a man who is a drunk or a drug addict.
I’m sure there is much more. Maybe my musings will spark some ideas in other people. In the end, though, I’ll bet that both men and women seek to change each other equally. Or, if we could find any data about this, we might find that. But I think it is a tendency that all of us have to one degree or another, but that it is not related to gender.
That’s just a theoretical approach to the problem. Now someone could go out and analyze plot lines in various stories and see how often it comes out one way or another. Also, you could look at a sample of relationships described in the psychological literature and count how often it looks like one or other gender is doing more of the trying to change.