There are at least a couple of factors I see as relevant: choice, responsibility, and the notion of giving them a chance to live.
Children, necessarily, have much of their life controlled for them. They are not allowed to make a lot of important choices for themselves, whether they want to or not. So, it is important for those making choices for them to make the right ones, to justify not allowing them that control. I'm not sure I'm quite articulating the concept here, but...
It is the explicit social, legal, and moral obligation of parents to appropriately care for their children. In a broader sense, it is a general obligation of society to care for the weak, helpless, etc.
Part of why the death of a young person is a greater relative tragedy today is that they have greater remaining potential lifespan, but part of it, in many peoples' mind, is that they have not yet had a chance to experience various major things. You'd feel a little sad for someone who, for example, died without ever having been in love, even if the person is 83, right? A little kid has missed a lot of experiences.
The thing I wonder is why humanity didn't insist that the superhappies refrained from acting on humanity until they had a better understanding of us. They made a snap judgement, that was obviously incomplete given what fraction of humanity opted for suicide under their plan--given more time, they likely could have come up with a plan that would reach their desired aims (not being made unhappy by humanity) with a minimum of distress to all parties...