Sorry for the delay @sylph. Been rebuilding my home and only got back on steem today.
firstly a child is a consequence of a parents actions, ergo responsibility for it exists with them logically by cause and effect chains of action. you can only have an actual obligation to something you agreed to, or as a consequence of what you have done. BTW, if you are going to make an analogy, at least make one which has the same level of resolution as what you are arguing against, otherwise you're not actually making a logical point, just a strawman.
Secondly, you pretty much missed the point I was making entirely, and then made it for me in your last paragraph. You reacted to an old saying (I can't find its origin actually, really irking me), one which means effectively "don't put everyone else's needs before your own, otherwise you will get burned". This excerpt does well to explain the meaning of the phrase (though the source is albeit a bit pants):
Your hair is singed from all the times you clipped your own wings just to make someone else happy. Your fingertips, blistered from all the times you forgot about your own needs and gave away what was meant to be yours. Even your voice has been touched by the flame, no longer strong, but shaking and raspy from all the times you wanted to say no, but said yes.
from http://www.yourownlife.org/not-required-set-fire-keep-people-warm/
Also, as a point of order: Violence is not the same thing as aggression. This may seem like mere semantics, but it is an important distinction. Aggression requires the initiation of violence. It does not include violence caused by defending from aggression. Its why libertarians and voluntaryists tend to follow the NAP not the NVP, or pacifism.
What is an "undue burden" then? Because that definition is critical if you want to enact a high resolution solution to society. Its not trivial at all to decide, because it doesn't just vary between culture or society. It varies between individual people within those societies and cultures, and that is the crux of the matter.
It's worth noting that many societies do believe death is necessary, nay laudable, and have done so over time. We may consider it barbaric to think human sacrifice is needed, but many cultures used to and some of our own still do. We praise soldiers, and sing to their glory when they are sent to bleed for our nation's interests, then abandon them in red tape once their minds or bodies are spent. All for that lovely oil that fuels and makes so much of our modern life. Oh sorry, that's right, it was "to protect our freedom" we killed people, then let our government take away those freedoms it so vociferously claimed it had to protect for us. Now apparently, its job is to protect us from those freedoms instead.
Your last paragraph is quite eloquent, and as I said, is the proper interpretation of the saying that you were rebutting. So I'm glad you at least understand the proper interpretation of the phrase, even if you didn't realise that is what the saying meant.
I also will agree that Kindness is a virtue, but Public Welfare is not kindness to my mind. It is a dangerous trap, disguised as something much shinier and tastier, and when you bite into it the jaws spring shut. Charity is kindness, but charity is voluntary, and that is why it is actually kind. A person actively wanting to improve another's lot? That works.
Welfare is not this. It is a mandate of how much one must be willing to sacrifice, and how it must be spent, all with no regard as to whether or not that individual consents to it. One must accept that fact to move past the concept of public welfare via the state being for the good of man.
Otherwise one must justify acting unethically to be ethical, and be able to do it all the time for every action taken by it.