Some people argue that a fertilized egg is alive and has the genetic material of a complete person, therefore it is a person. This argument, that a fertilized egg is a person because it has the DNA of a complete person, is not accurate or reasonable. To see why, consider the body of a recently deceased person. When a person dies, there are cells within the body that continue to live and express their DNA up to about three days postmortem, or longer if the person was an organ donor. This phenomenon, of cellular life persisting in a body without personhood, is what makes life-saving organ donation possible. (A dead heart is not going to save the life of someone who needs a heart transplant. A person who needs a heart transplant requires a living heart gifted by someone who already died and thus no longer needs their living, functioning heart, that by definition has living human cells with complete DNA.) Because a dead person is dead even if there are living cells in the body, the argument that “a living cell with a complete human genome is a living person” must be false.
According to science, life doesn't begin; it continues. A sperm is living cell but not a person. An egg is a living cell but not a person. They are both alive, and when they merge together into one cell (a fertilized egg) they continue to live. Life does not begin at fertilization, rather fertilization is the continuation of life.
A fertilized egg is called a zygote. When a zygote is alive, and when it has human DNA, it is a human life like any of the cells comprising a human body, and like each cell in a human body, a zygote is not a person. More than two-thirds of all zygotes naturally fail to implant in the uterus and thus never develop into new human people. Of zygotes that do successfully implant in a uterine wall, roughly half survive and develop into fetuses by 12 weeks gestation. Each fetus becomes a person when the cells forming the developing fetal brain are able to provide the body with the ability to think and feel emotions. From the point a developing body gains a person within, the body continues to develop and to mature until adulthood. Then the body begins to degrade with age. Eventually the body degrades to the point that the collective of trillions of human cells can no longer sustain a brain capable of thinking or feeling emotions. That point is the death of person, but not the death of every tiny human cellular life in the body left behind. Those tiny human lives will live up to three days after the person died, or longer if the person was an organ donor. The point is that your cells, the tiny human lives that form your body, can live before and after you do. Your life as a human person will end when you lose the ability to think and feel emotions, which happens before the last of the cells with your DNA die. Conversely, your life as a human person began when cells with your DNA provided your brain with the ability to think and feel, which happened 23-27 weeks after the first of the cells with your DNA lived.
There is such thing as a body devoid of a living person but not devoid of cellular life, and there is a timeframe during pregnancy when this phenomenon is present. From the beginning of pregnancy up to between 23-27 weeks of gestation, within a womb there exists a body of living cells that does not contain and has never contained a living person. Abortion up to this point is not murder because there is no person in the womb. After this point, there is a person in the womb, and the only ethical way to end a pregnancy in this case is to separate the two people (see caveats in The Third Question).
In summary, people have minds. Zygotes do not have minds; ergo, zygotes are not people.