The sperm and the ovum can’t become a brand new human being on their own.
However, the moment conception happens, we have a brand new human organism, completely separate from the parents on a genetic level.
Hence the focus on ‘conception’.
Actually, an ovum can spontaneously become an organism on its own. And now scientists are achieving the transmogrification of a particular sperm cell, to transmogrify it into a totipotent zygote cell/organism.