Is It True that a Cynic is Just a Realistic Optimist?

One thing that strikes me about libertarianism is that it seems premised on the belief (and I may be misunderstanding, so jump in if I am) that individuals, when left to their own devices, and given a free market to operate in, will naturally act in their own self-interest. This is, I'll admit, one of the reasons I'm having trouble understanding how people who call themselves Christian Libertarians reconcile those two things. If people are inherently bad and need redemption through Jesus, how can letting them act in their own self-interest be a good thing? I'm not asking to be petulant; I really don't get this and I think if someone could explain it, I'd totally have a lightbulb moment. But, setting aside the Christian Libertarians for a moment, I remain fascinated by how hopeful the libertarian philosophy seems to be about the nature of humanity. Will people, if given the chance, act in their own self-interest? I think here's where we get into the deep misunderstanding I have about what libertarians mean by "individual." It seems to me that they mean "each person as utterly distinct from each other person." But, clearly, there are all kinds of ways that we perceive ourselves as parts of larger groups. I mean, look at the whole 'alpha male' discussion. That discussion makes no sense unless we all understand that men perceive themselves to be in relation to each other in some way and that many of them want to be in positions of power within those relationships. And, from the moment we're aware of ourselves as beings, we're aware of ourselves in relationship to other beings--family, community, etc. And, clearly, people will act in ways that are not in their own self-interests if they perceive it to be necessary to the well-being of the group. As well as not perceiving myself as utterly distinct from the people around me (though, there are days when I wish it was so), I also wonder what libertarians do in the face of children. Let's simplify the libertarian creed to "I do what I want as long as it doesn't prevent you from doing what you want--and visa versa." (Fair enough?) And let's say that most things are now privatized. There's no public aid, there's no Head Start, there's no public schools, even. And taxes are exceedingly low because no one pays the government to fund any social programs. Now, let's say that there's a five year old kid whose dad is gone and whose mom is on drugs. All of her money goes to drugs, except for food and rent money. But, she wants her kid to stay with her. So, she won't voluntarily give the kid up. But she won't spend her own money to send the kid to school. The child cannot, obviously, afford to go to school himself. He's a kid. He's got no income. Do libertarians let the child suffer? If so, why do the woman's rights take precedence over the rights of the child? If not, how can you justify taking the resources of the woman and assigning them to the child? And, once you've said that a parent has an obligation to take care of his or her offspring, aren't you acknowledging that we aren't individuals utterly distinct from the people around us but are also important parts of groups to which's well-fare we contribute?* I'm more and more convinced that libertarianism is a really important strain of political thought. And I believe that they're right about many of the ways that the government oversteps its bounds and barges into our lives. But I'm nervous about their unabashed faith in human nature--this belief that we'd all act in our own best interest if we could--and I can't believe that I'm not a part of groups to which I owe my loyalty and it to me. I just can't overcome that. *Something is hinky about that sentence, but I can't figure out how to fix it. I hope you see what I mean.