A telling statement. Governments grant citizenship in the context you present, so you seem to be saying that the "full gamut of rights", including, presumably, the right to live, is granted by government.
Evidently there is a fundamental disagreement here, the crux of which is the notion of inalienable rights. The founders of our country recognized the importance of acknowledging the existence of these, and the government's proper role in safeguarding them, not granting them. Our laws recognize that non-citizens have fundamental protections under the law. Their citizen status is not relevant to the consideration that they should not be subject to acts of murder.
For abortion to be defensible, you have to argue from a position of denying that the unborn child is not human life, or, if it is, there is a class of human beings that are exempt from the basic protection that we afford in the vast majority of cases: the right to be left alone and not killed by another. Our society, and others, make a case for some conditions under which the life of another human being may be taken, but, in their essence, these are based, in one way or another, on the notion of self-defense. Other than in very limited cases wherein the mother's life is 100% at risk of death from the pregnancy, it is difficult to see that abortion on demand meets the criteria established for the cases wherein taking of human life is justified from an ethical viewpoint.
However much I may appreciate the rhetoric of the Bill of Rights, and I do--in the real world citizenship is an earned right.