You cannot rationally hold the belief that people can be allowed to have as many children anytime they want and that all children will be provided for regardless of the ability of their individual parents to provide for them. Such parents have shown they have no limiting factor, so the end result is that all children will be poor as you divert greater and greater resources from parents who act in more responsible ways to those who don't.
It's also a curious way to characterize it that "we're consistently condemning the children for the sins of their parents." Seeing as "we" had nothing to do with creating the plight of these children, "us" not acting to change it is not us condemning them. That's like saying "we" are responsible for that child that fell into the well and drowned recently as we didn't save him. Or that "we" are condemning that fat guy to an early death because "we" aren't forcing him to eat salad and go to the gym.
Not to mention that for every poor kid in this country (assuming you meant the US when you said "the country") there are a five to ten in southeast Asia with a lower standard of living. How do you justify tapping the productivity of a Boeing working in Renton to provide for a poor kid in Mississippi who has no more connection to that worker than a poor kid in Cambodia, while simultaneously not ensuring that that Cambodian kid has the same standard of living and opportunities you want to give to the Mississippian?
I will agree that it's a very unfortunately situation, but I'm not going to lower the standard of living of my own family that limits their chances of having their best life so as to provide for the child of a stranger who doesn't give the same care and thought to me and mine.