I have always thought that the phrase that was popular some years ago "science tells us that life begins at conception" was odd, and misunderstands what we know

I have always thought that the phrase that was popular some years ago "science tells us that life begins at conception" was odd, and misunderstands what we know about life from science. Life does not begin at conception because it never stopped. The sperm and the egg were both alive at the time of conception, and were life that split off of the collections of cells that we call the parents. Those parents were in turn conceived of live cells (again: a live sperm and a live egg) that came from their parents. The whole point is that life is one big unbroken chain going back to some first cell (and at that point what is "life" gets complicated). Rather the whole thing is about a "human life", as in when do we decide that this ball of cells is a separate individual deserving of the protection we give "people". And that is almost completely arbitrary, and science can offer no input on this at all. Why is a fertilized egg a person? Why are the skin cells that have scraped off on your keyboard not a person deserving protection? If you start chopping bits of a person off (I am not recommending this), is the severed limb not a person? If you could chop off the head and keep both that and the body alive, would those be two people? Or would only the head count as a person?