Abortion and Age-reckoning

One of the arguments for abortion is that we don't count someone's age from the date of their conception, or of quickening, or some other point in utero. We count age from their birth. If we really believed human life began at an earlier stage, we would recognize it here and we simply don't. I've never found this argument convincing.

1) We count age from birth because this is the child's introduction to the public world.

2) Birth is a very dramatic phenomenon with immediate objective results and so supplies us with a very obvious point of reference (whereas conception and quickening do not).

3) This argument would mean that a fetus at nine months gestation is not really a human being, and can therefore be killed without repercussions. Very few people would accept this. This is significant since the whole point of this argument is based on an appeal to common perception and belief.

4) Plenty of cultures throughout history have reckoned age according to the approximate time of conception. This has been common in east Asian cultures for example, like China, Korea, Japan, Vietnam, etc.