Anarcho-capitalism: Succint Description of my Opposition

1- Anarcho-capitalism (AC) says that abortion is fine as the mother is fully within her rights to expel a predator.

Does one have the right to expel a guest for no reason. No, one doesn't. And the child is a guest whom the mother willingly invited. And the fetus has to be assumed to be conscious from the date of inception otherwise those who oppose the statement have to show how the fetus became conscious.

2- AC says that only rights are property rights

I murder a child in an area which no one claims to be his/her property. If the child is not his/her parents property then no property right is infringed (assuming child is not working). So murdering a child is ok.

3- AC claims that parents rights over their children are limited

I capture an animal. Don't I have the right to kill it, torture it, or recapture it if it runs away. When I can have such rights over a creature which can exist independently of me, why can't parents have such rights over their children who, unlike most things available in market, are created from their bodies and only their bodies.