The author's thesis is that children are important to the well being of society. A necessary good. If you accept the thesis that over time new children are necessary for the health of the society you live in then you must accept that those who choose not to bear the full costs of child raising are engaging in "free rider" behaviour.
Not necessarily. Those who make that claim would seem to be operating on some type of doomsday scenario. Perhaps that argument was valid back in the day, when the survival of the species depended on everybody cranking out as many juniors as possible, but it is not obvious to me that such measures are required at this point in time. I have seen here no breakdown of costs, no analysis in any depth, nothing other than some hysteria about the baby boomers. Furthermore, any analysis would have to be made in context: namely, the realistic expectation from today's generation. Sure, one can go raise kids in some sort of commune to the end of generating a captive audience, but what purpose does this serve other than feeding one's ego and possibly ending up on the evening news. Twisted.
From glancing over the posts, I perceive that there is an element making the claim that it is ultimately one's socio-moral obligation to procreate. Well, there seem to have been quite a few socio-moral obligations out there, from indulgences to subjecting oneself to having one's heart ripped out. The beauty of America is, the extent of one's socio-moral obligation is contextually up to interpretation and not the decision of a self-chosen arrogant few.
If you have kids, and you don't pay 100% of the costs of raising them (i.e. if you accept subsidies from other people's taxes to pay for schools, etc), you are the free rider.