I'm with Jack - I think it's Jack. Bringing a kid into the world places an obligation on the parent, not the child. It's not - exactly - a tort, but it's very similar. the parents decide - amongst themselves, with no input from the child (How could there be?), to place a self-owner into a state where they are incapable of taking care of themselves. They had plenty of chances to back out of this obligation, and they didn't take them.
Take chores, for instance:
The "child is obligated to the parent" school says that these chores should be done to repay that obligation - "I brought you into this world, therefore, you're my slave until you're 18."
The "parent is obligated to the child" school, however, says that these chores should be compensated, because the child is not obligated to do them - but the parent is not obligated to provide an allowance, either.
Now, clearly, one of these strategies is more in light with libertarian thinking and the concept that a child is a self-owner who has rights.
