Except that body is half her body,
Which half exactly?
Also, out of curiosity, when is abortion no longer allowed in your opinion? What exact time and date after conception?
The only logical point to consider a new life to exist is conception. The argument here is simply about under what circumstances it is considered acceptable to kill a baby.
Arguments about "dependence", "Its just a ball of cells", "The nervous system has not yet developed" and so on are simply sophistry used to deflect the argument away from this fundamental issue.
A good starting point would be to start from the proposition that the only circumstances where it would be considered acceptable to kill (Or allow to die) a baby six months before it is born are those where it would be equally acceptable to kill (Or allow to die) a baby six months after it is born. and see where the discussion takes you.
For my own part, while I do not agree to abortion for convenience there are other circumstances where I would consider abortion/"Liverpool care pathway"/etc entirely acceptable. (And would be happy to see it applied in circumstances where it currently doesn't)