There are a dozen explanations out there why the American birthrate is below replacement, and why middle-class and above white females in particular are having fewer children, and many seem quite plausible. There does seem to be a worldwide trend that as countries become more prosperous, and couples believe their children might have access to higher status, they limit the number of children they have. Secondly, optimism about the future seems to be a driver of having more children.
I wonder if there is a fairly simple but overlooked factor, the inertia of one cultural idea. From the age of about fourteen on, girls are not only told "Don't get pregnant," but "Smart girls don't get pregnant," which carries a double meaning of smart=birth control/less impulsive and smart=intelligent/ career-driven. It becomes something of a default position, and may embed quite strongly. Though the original intention of "smart girls don't get caught" is not the same kind of smart, it does tie in with the idea "Upwardly mobile women have fewer children," or "this is not a good time in your career/education to have children," as above. They then have all the decision-making influences of opt-in versus opt-out. A default position of opt-in results in more people being on lists as organ donors, for example. In previous generations one did not have to opt-in to having children. That was the default. (Exceptions abound, but I think we recognise this general cultural difference between yesterday and today.) Today's default among white middle class women is that one has to specifically opt-in to this childbearing idea.
"Smart girls" is just a song playing quietly in the background, a gravitational force that is more of the explanation than we credit.
I have written the above as if the males have nothing to do with these child-having decisions, which is not true. Men may even be equal drivers in decisions to have no children at all. But I think women have enormously more say in how many children a couple has. The Right Number is achieved and she vetoes any suggestion of more.