Because it's built into us to protect children? Seriously where would society be if it *didn't* place a greater focus on the wellbeing of our chioldren then of the current adult generations? The whole mantra that 'our children should live better than we' is a common troupe that exists cross culturally.
I think it is also indicative of Humanity's inate ability to see reason. In that survival of the species and the logic that children (even those not related to us) are the future and therefore they represent an investment into the continued prosperity of the species.
So because they represent this investment in the future, we should give them every possible chance to grow and give them the absolutely best environment to thrive and develop so that they may not be so jaded as we towards the cruelty that is life and experience.
So, from a rational perspective, children are the most important members of society because they represent that which will be our legacy as a culture and species. I think each human more or less understands that and thus wants to create a better world not for ourselves but those that will inherit the Earth from us.
But that's my two cents <.<
That beingh said I'm stating the philosophical 'ought to' as opposed to 'what is' scenario. The world is a shitty place to grow up. Regardless of where you live. Ecological catastrophes, widespread famine, rampant disease (albeit better than in some centuries previous), political and civil strife.
But I think the average person knows that the world can be better and realise that it's their duty to act as moral and decent human beings if only because future generations deserve nothing less.