Two problems with that view:
1. A child can be extracted prematurely, at varying degrees of risk, and be made independent of the mother.
2. No child is capable of sustaining itself immediately after birth. It remains dependent upon others, although not necessarily the mother.
It sounds like you might agree with one property of rights--that one individual's rights cannot interfere with another's (if a thing does conflict, then such a thing is not a right).
Still I wonder what a right is, and how we can examine a thing to determine if it has any.
It has not happened yet, but the day is coming when an in vitro fertilization will be followed by "in vitro" gestation to full viability. The artificial environment will be a lot more complicated than a test tube, but I think that most of the function will be automated, so it will not require a lot in the way of attention.
I believe that the product of this process will be as fully human as you or I. And once it happens, even a single time, the argument about viability is totally and permanently destroyed, as it deserves to be.