Whatever its merits, the welfare state is a disincentive to childbearing. Each generation of workers pays for the retirement benefits of the generation ahead of it. The system is powered by babies, who grow up to become productive little FICA contributors. But even if you never have children, someone else's kid will eventually pay for your Social Security benefits.
The idea of welfare as a disincentive to childbearing is an interesting twist on the argument that one of welfare's policy outcomes is a disincentive to work (i.e., why work when I can just sit and collect a check).
Of course, the author's argument that "the welfare state" discourages baby-making directly contradicts the old "welfare queen" argument that welfare recipients had more kids to get more benefits. This illustrates the rhetorical danger of conflating with each other two public programs with vastly different target populations and social constructions (see Ingram and Schneider's book, or this much shorter essay, for more on these concepts). Social Security targets retirees and is (mostly) positively socially constructed, while the federal cash assistance program popularly known as "welfare" (and less popularly known by the unpronounceable acronym PRWOA) goes to younger, and, according to a prominent social construction, less deserving population. In other words, don't confuse the welfare program with the welfare state.