Like most things in biology, "conception" is a process. If you want to break it down and go with the first mitosis instead of the penetration of the egg by the sperm, I don't have a real problem with that. I think the formation of the zygote, which has in its proneuclei the DNA of the father and mother, is a better definition, but if you want to wait 12 hours that's fine by me.
And call me when a tumor has the potential to develop into something we can all agree is a human/person.
Whether you agree or not is one thing, but the argument is not difficult to understand.