The main reason behind this is the return of patriarchy. No, I don't mean the scent, I mean the philosophy. As the article says,
Patriarchy does not simply mean that men rule. Indeed, it is a particular value system that not only requires men to marry but to marry a woman of proper station. It competes with many other male visions of the good life, and for that reason alone is prone to come in cycles. Yet before it degenerates, it is a cultural regime that serves to keep birthrates high among the affluent, while also maximizing parents’ investments in their children. No advanced civilization has yet learned how to endure without it.
Because the affluent tend to be more conservative (also, those who tend to practice patriarchy are more conservative), then they rule the dialogue. This is a bit simpler than the explanation in Foreign Policy, but I don't want to write four internet pages about it.
This is already being seen among some groups. Of course, most known for high birthrates are evangelical Christian groups, especially us Mormons. We get married relatively young (it's creeping up there, but it's still much younger than the national average) and we make sure we have lots of kids, the better to multiply and replenish the earth with. This is also one of the reasons why the US is in dire need of immigrants. I know there are groups out there who want to get rid of all the Mexicans and put up a wall, but they're going to be the only way we can finance Social Security, Medicare, and continue to live the lifestyle we are. Without them, we'd be a nation of Wal-Mart greeters - sure we're friendly, but in the end we can't even get the boxes down from our collective shelves. This also means that, with the imminent collapse of welfare states (it will happen when the younger generations can no longer shoulder the burden of an incredibly top-heavy society), there will be a return to the conservative values of doing things yourself and not relying on the government for everything. However, what if there's a countermovement? Perhaps the next younger generation will want their Medicare?
The key difference is that during the post-World War II era, nearly all segments of modern societies married and had children. Some had more than others, but the disparity in family size between the religious and the secular was not so large, and childlessness was rare. Today, by contrast, childlessness is common, and even couples who have children typically have just one. Tomorrow’s children, therefore, unlike members of the postwar baby boom generation, will be for the most part descendants of a comparatively narrow and culturally conservative segment of society. To be sure, some members of the rising generation may reject their parents’ values, as always happens. But when they look around for fellow secularists and counterculturalists with whom to make common cause, they will find that most of their would-be fellow travelers were quite literally never born.