The essential properties of a person are sentience, the capacity to feel pain and pleasure, sapience, the capacity for self-awareness, and individual personality.
Biological independence, the ability to function as a independent entity or "organism", and human genetics are the essential characteristic of a human organism: Brain-dead but still breathing bodies, for instance, are human organisms, although lacking sentience, sapience and personality they are not persons.
An embryo has only one of these essential characteristics and none of the essential properties of a person.
Morality is built on empathy: We do not wish another being to experience that which we would not wish to experience. Since we ourselves do not (typically) wish to experience pain and suffering, we do not wish another being to experience pain and suffering, hence we object to, for instance, cruelty even to animals.
There is simply no point of similarity on which we can feel empathy for an embryo: It cannot experience even pain and suffering, much less the awareness of mortality which is entailed by sapience. I cannot feel empathy for something that itself cannot feel, cannot think, cannot be in a mental sense. I have no more rational justification for empathy for an embryo than I would for an amputated finger.
No empathy, no moral status.
I have empathy for all sapient beings, human and non-human, and I disapprove of anyone who does not have empathy for all sapient beings, I strongly disapprove of anyone who does not have empathy for all sapient humans and I violently (to the extent of supporting coercion through lawful means, i.e. police, courts and prisons) of those who would cause suffering to any sapient being, that is pain against his, her or its will.
(I admit also to a degree of speciesism--all other things being equal, I have different empathic attitudes towards non sapient members of species typically sapient, especially my own species, then towards members of non-sapient species. Since this speciesism enhances moral status, I don't see it as problematic.)
Most importantly, I have empathy for a woman--a fully human, fully sapient being--who is pregnant against her will. If she does not wish to be pregnant, then pregnancy will by definition cause her suffering. When I balance that suffering against the physical impossibility of an embryo suffering, I can come to only one conclusion: I must not only permit abortion, but I have an active duty to ensure that any woman who wishes an abortion is able to receive one.