Makes one wonder how much of the funds contributed by older generations and "borrowed" by fed.gov were ultimately spent on programs (education, WIC, AFDC, CHIP, food stamps, etc, heck, even basic long-lived infrastructure like roads, bridges, and parks) that benefitted the younger generations.
It's true that parents support their children while they grow up, just as their parents did for them, and their grandparents did for their parents. Such is the usual order of things. To the extent that these government programs you mention provide resources that would otherwise fall to parents to pay for, then the parents are the ones who benefit by not having to pony up.
If you (or anyone else) mean to imply that it's OK to "indebt" your children to pay for their upbringing, then I think you're mistaken. First off because most of the money "borrowed" from the youngsters through SS went to stuff unrelated to their childhood, and thus isn't applicable. But even if we assume that it is, that there's some magical system whereby children can pay their own way through childhood by borrowing against their future, this idea still falls flat. To have your upbringing funded by your parents (as has happened from the beginning of time through the present) and yet demand that your children fund themselves (after the advent of this magical borrowing system) is to shirk your responsibility.
Mathematically, there must be one child rearing effort funded for each generation that lives. Every generation is obligated to fund one round themselves. Whether we choose to pay it forward by paying for the rearing of our children, or pay it ourselves through some sort of borrowing scheme, it ultimately doesn't matter so long as each generation pays for one round of child rearing. What this borrowing scheme represents is a way for the older generation alive today neither paying for themselves nor their children. They will pay for none and leave it to others to make up their shortfall.