You’ve got this exactly reversed, I think. The reason there are so many extra pet animals is because of the people who BUY them and create an industry of profit on the ‘image’ of having a pet vs useful care of an animal. Those millions of animals going into shelters are like factory farmed cattle: driven by demand (the billions spend by pet owners). So, does this apply to children? I hope not, but I’m afraid it probably does to some degree. Maybe not as much in the demand for children per se, but in the industrialized creation of demand for sex in advertising, as well as blind perpetual economic and cultural expansionism and romanticism of Happy Families that don’t actually exist.
On first glance, it seems obvious that high populations are a resource problem, but from nature’s perspective, useful species contribute to the spectrum of life. If humans were to be raised to be contributors to the planet, rather than consumers, then the issue of how many or who has children would kind of flow with other efforts and goals. The way we do it now (blind ignorance of planned parenting and responsibility buried behind commercialized market saturation with sex, romantic love and mating egoism) is influenced more by profit-based corporations and branding (“child-free” vs. “yummy mummies”, etc.) than conscious thought (especially for parents under the age of maturity — 25). The current state of DNA research should have some significant influence, as well as parental fitness testing and education, but that might infringe on someone’s ‘freedom’ to be idiotic and force their idiocy upon innocent children (see pets, above or any reference to religion).