It already does. If a patient is brain dead, we usually take it off life support. The mother of a fetus is effectively a life support system, from the fetus' perspective. Being human is not simply a matter of DNA. Ask a twin if they're an individual, separate from their sibling. It's a matter of cognition, and there are grey areas. The closer to human levels of cognition we perceive, the more the death of an organism troubles us. Seeing a dog die is more traumatic than seeing a mouse die, because dogs' behavior leads us to believe that they understand and value the world in ways that are similar to ourselves. Conversely, most cultures execute certain criminals, depriving them of their lives because the values they place on community norms shows that their ethical understanding is outside of the bounds of what is accepted as human norms.
Up to a certain point, a fetus does not have a sufficiently complex brain to be able to encode a sufficiently human model of the world for many people to consider it human. It does not have language. It has not encoded experiences. It is not aware of others. Meanwhile, it's life is parasitic to the mother, who, in almost all cases, fully meets the qualifications for being human. Since we are anthropocentric, outside of specific indoctrination, people tend to value the continued life of the mother more than that of the child. If the mother accepts the fetus as a part of herself, it should be protected, as we would the mother. But, if the mother chooses otherwise, her claim to her body and health are superior to other people's claim that she should risk both for an ideal that she doesn't share.
If it were possible to transplant a fetus, perhaps the arguments would be different. Perhaps the anti-choice contingent should spend their money on that, rather than campaigns to traumatize young women who are in a situation that is untenable, often through no fault of their own, where their lives must end, regardless of their dreams, aspirations, and preparations otherwise. The family and children they may have planned might not be born because the pregnancy they did not want cut them off from the community they would have otherwise joined. Maybe they are cut off from their family. Maybe they wind up never going to college, or even finishing high school. Maybe rather than being a self-sufficient engineer raising two honor roll children with a husband, she winds up as a single mother in a series of dead-end jobs, with no family leave, so that her child has to raise himself in the kind of environment a minimum wage job affords. It's true that a child like that can turn out okay, with a mother so dedicated to the child's welfare that she denies herself the opportunities to fulfill any of her own dreams, but a woman with that attitude is unlikely to have gone to the abortion clinic in the first place. Whether a woman decides the wrong time to have a child, the wrong father, or a she feels that the risk to her physical or emotional life is too great, society should respect her decision.