“Human organism” is a scientific concept. It starts at birth.
“Human personality under the law” is a cultural and legal concept. It cannot be determined using scientific methods.
For the vast majority of history most live adult human beings were not “persons” with rights under the law. FTM, until not that long ago a married woman in this country ceased to be a “person” legally during her husband’s life. The two on marriage became legally one person, with the legal actions of that person controlled by the husband.
Name me one person in the history of humanity whose existence started at birth. In other words, one person who was not conceived and then nurtured in a human womb.