With great respect to the Talmud, we can't know exactly when life begins. If we believe in God and the existence of an immortal soul within us, we must err on the side of caution. From the point of view of the human intellect, the most obvious time for God to impart a soul is at the moment of conception. That is when the most profound physiologic changes occur. That is when an incomplete genetic package becomes complete with all the code of a complete human being.
How about when it is too late for an embryo to become a twin?
At conception, the soul of life force is proven 'there' by the action of organized growth, as in will exercised to live. What we do not have proof of is the presence of the human spirit with the soul of life, but as in your 'cautionary' word, we ought assume the spirit is present as soon as the soul is present. Until someone can prove the spriit doesn't take up residence with the soul at conception but at some later date, it is an arbitrary selfish (I would say self-appointed godhood) assumption to kill the newly conceived claiming 'no human is there yet.'