It doesn't negate the claim that parent made though. "Your kids" had a wider meaning (and still has in a lot of places) but the principle remains: an adult had to provide, and protect a limited number of (usually related) kids to be cared by those of them who survived later in life.
That's not how it works unless you try to say that adults in general are interested in kids survival. This would be true but it's not what drives larger efforts, and resources allocation. For that there are always related kids which get the most of one's resources, and other kids which may get something sometimes. And there are your elders and others' elders as well. Actually, there are plenty of countries where pensions either not a thing, or too small even for basics. I lived in some of them and I dare to say I know what I'm talking about.