I couldn't disagree more with you, but I quite agree with the author of your article. Who rightly points out that taking absolutist, unconditional approaches to abortion is a terrible way of approaching the issue, whether it's Hillary doing it or Trump. And that actually once you get past that, there's a wide consensus among Americans on things like banning abortion in the third quarter.
As for your 'logic', yes, you can say life begins at conception, for a certain definition of 'life'. If you call ending a first quarter embryo's life murder, you should also call the killing of animals murder. On the other hand, during the third quarter, the foetus is viable outside the womb, so then killing it is more comparable to killing a newborn, which is why it's illegal almost everywhere except for extremely grave reasons. Life as such may be a binary concept, but the development of a baby in the womb is a gradual process, so it's only natural that throughout the process, the balance between the mother's rights and the baby's rights shifts considerably.