You share as many genes with your siblings as you do with your parents and your children. Yet not only is there no legal responsibility to help your brothers and sisters; even the perceived moral responsibility is pretty weak. Socialists often lament that society should be more like a family, but if we use fraternal obligations as a benchmark, libertarians could hardly object.
Now suppose someone were to argue in favor of what I'll call fraternalism - the view that that people ought to be legally responsible for their siblings' well-being. What objections could one raise?
1. Moral hazard. If I'm my brother's keeper, he has less incentive to keep himself. Fair enough, but (a) only Non-Bleeding-Heart Libertarians find this is a decisive argument against the welfare state, and (b) you could limit responsibility through e.g. time limits, like "You only have to let your brother sleep on your couch for a year."
2. Desert. Perhaps more successful siblings deserve their success, and less successful siblings deserve their failure. Fair enough, but a lot of success depends upon innate ability, and once again, who besides Non-Bleeding-Heart Libertarians is completely comfortable with the idea that abler people deserve to be richer?
3. Rights. Suppose your sibling tries hard, and you're better off just because you got lucky. Nevertheless, you don't feel like helping him, and don't see why you should have to. Why should he have a claim on you? Who made you his slave?
You can probably see where I'm going with this. Arguments against fraternal duty closely parallel arguments against the welfare state. If you aren't obliged to help your brother or sister, why are you obliged to help strangers (or at least strangers from your own country)?
For that matter, if you aren't forced to practice familial nepotism when your brother asks for a job, why do immigration restrictions force us to practice national nepotism when a countryman competes against a foreigner?