Why does the Catholic Church hold that conception is the readily identifiable beginning of life, and insist that this is readily observable even by non-believers? I explain in my essay as InsideCatholic:

Conception is the point when the new organism begins to exist because it is the first moment at which a single organism capable of developing as a member of its species — in this case, the human species — comes into being. Before conception, neither a sperm nor an ovum can develop into anything at all on their own. After conception, there is no point that could be identified as the beginning of a new organism, because every significant stage after conception is only the transition from one physiological stage to another. None of those steps could be considered the “beginning” of development, anymore than we consider puberty — a major developmental stage — to be a stage that defines human life (however much we may joke about it).