Self ownership is the most basic human right. And that fully implies and requires not being forced to pay for, work for or support the desires, goals, wants or needs of others.
True. If she wants something- then earn the damn money and pay for it. Her so called right is also our right to refuse handing her or anyone money they do not earn.
There are non-contract obligations too. You can incur obligations upon yourself by causing someone else's condition of dependency. For instance, if someone carelessly caused you to lose the use of your arms, they would, as a matter of strict moral liability, be duty-bound to pay for the surgeries or therapies or whatever to restore the use of your arms, or compensate you for the lifelong loss of your arms.
Parental obligation arises in this manner: the parents caused the child to come into existence --- in, obviously, a dependent state --- therefore they owe him or her parental support.
Nor can they invoke a "right" to abortion even if the pregnancy were caused by a non-consenting act, e.g. rape. Upon the onset of his existence, the unborn child has the same right to self-ownership, and therefore has the right not to be assaulted and killed. The developing child has the same right to simply go on living without being slain.
After the child's birth, that parent's only duty would be to arrange for somebody else to support the child, i.e. adoption.