The biological machinery for life is in place always, and the only time the biological machinery was started was the formation of the first life form that was capable of replicating itself developing in the primordial soup. The rhythm of life has been placed in place in the machinery, and since it has been a continuous flow of life continuing. The machinery is not placed in place with each conception. Without the parents' zygotes, the conception would not happen. So Zygote is the placement of life in in the machinery? No, because zygotes could not be produced without sexually mature adults. So sexually mature adults are the point in which life's machinery is placed? NO, childhood precedes adulthood; without children, there would be no adults. Children are etc etc etc.
To claim that life starts at inception, is false. Life started some beeeeelyuns of years ago, and it never stopped happening. In one continuous connectedness, but in many different threads.
I agree, however, that personhood starts at an arbitrarily designated spot in the development of the fetus, or at birth, or at 18 when you can get married, vote, consume alcohol and drive a car, and own a gun. I mean, what other proof do you need to personhood than the ability to be responsible before the law. You can never charge a chair or a carpet with murder or with embezzlement, and put it to jail, can you. The same with a foetus, and to a lesser degree, the same with a child. Children are adults with limited liabilities, when you consider who is and who is not a person.
But that's the law. If you talk about philosophy, however, and you are trying to define on philosophical considerations when personhood starts, your definition is as good as anyone else's.