No one said anything about forcing a child into conditions that rob it of its 'personhood' (which is still not very defined). Forcing the child would be violating its liberties.
At any rate, a fetus does have it's own DNA. Of course, so do plant cells, animal cells, etc. The fetus is attached to the mother insofar as it is biologically dependent on a specific person (that is, until it is separated, there is no substitute for who is responsible for it). A baby is not so attached.
Additionally, to say cells communicating form a recognizably human cognitive ability is not discriminating enough. By that definition, a great many things are human. What can a baby do that sets it apart from a fetus (at least in early stages)? One thing is language processing.
Your using this idea of potential way too loosely. A piece of graphite has 'potential' to become elements of cells or even DNA and develop into a nice, happy human being, but that doesn't stop anyone from smearing it all over a piece of paper.